Office 365 Hybrid with Outlook 2010 can't automatically setup outlook search fails

See attached for Outlook results

If I use the users credentials from my workstation, I get:
      Attempting to send an Autodiscover POST request to potential Autodiscover URLs.
       The Microsoft Connectivity Analyzer successfully retrieved Autodiscover settings by sending an Autodiscover POST.
       
      Test Steps
       
      The Microsoft Connectivity Analyzer is attempting to retrieve an XML Autodiscover response from URL https://pod51038.outlook.com/Autodiscover/Autodiscover.xml for user GraceC@tbqc.mail.onmicrosoft.com.
       The Autodiscover XML response was successfully retrieved.
       
      Additional Details
       Autodiscover Account Settings
XML response:
<?xml version="1.0"?>
<Autodiscover xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://schemas.microsoft.com/exchange/autodiscover/responseschema/2006">
<Response xmlns="http://schemas.microsoft.com/exchange/autodiscover/outlook/responseschema/2006a">
<User>
<DisplayName>Chan, Grace</DisplayName>
<LegacyDN>/o=ExchangeLabs/ou=Exchange Administrative Group (FYDIBOHF23SPDLT)/cn=Recipients/cn=31bab3aba16c44c4bddc00e07edfac29-Chan, Grace</LegacyDN>
<DeploymentId>1319c81a-79a2-4a22-b833-fb697e950ead</DeploymentId>
</User>
<Account>
<AccountType>email</AccountType>
<Action>settings</Action>
<Protocol>
<Type>EXCH</Type>
<Server>20c9d77c-5832-4244-b71c-da13134332ee@bergquistcompany.com</Server>
<ServerDN>/o=ExchangeLabs/ou=Exchange Administrative Group (FYDIBOHF23SPDLT)/cn=Configuration/cn=Servers/cn=20c9d77c-5832-4244-b71c-da13134332ee@bergquistcompany.com</ServerDN>
<ServerVersion>73C082E9</ServerVersion>
<MdbDN>/o=ExchangeLabs/ou=Exchange Administrative Group (FYDIBOHF23SPDLT)/cn=Configuration/cn=Servers/cn=20c9d77c-5832-4244-b71c-da13134332ee@bergquistcompany.com/cn=Microsoft Private MDB</MdbDN>
<ASUrl>https://outlook.office365.com/EWS/Exchange.asmx</ASUrl>
<OOFUrl>https://outlook.office365.com/EWS/Exchange.asmx</OOFUrl>
<OABUrl>https://outlook.office365.com/OAB/bffbef90-82fa-4f63-9994-4b33f4ab4abe/</OABUrl>
<UMUrl>https://outlook.office365.com/EWS/UM2007Legacy.asmx</UMUrl>
<Port>0</Port>
<DirectoryPort>0</DirectoryPort>
<ReferralPort>0</ReferralPort>
<AuthPackage>Anonymous</AuthPackage>
<PublicFolderServer>outlook.office365.com</PublicFolderServer>
<EwsUrl>https://outlook.office365.com/EWS/Exchange.asmx</EwsUrl>
<EmwsUrl>https://outlook.office365.com/EWS/Exchange.asmx</EmwsUrl>
<SharingUrl>https://outlook.office365.com/EWS/Exchange.asmx</SharingUrl>
<EcpUrl>https://outlook.office365.com/ecp/</EcpUrl>
<EcpUrl-um>?rfr=olk&amp;p=customize/voicemail.aspx&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-um>
<EcpUrl-aggr>?rfr=olk&amp;p=personalsettings/EmailSubscriptions.slab&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-aggr>
<EcpUrl-mt>PersonalSettings/DeliveryReport.aspx?rfr=olk&amp;exsvurl=1&amp;IsOWA=&lt;IsOWA&gt;&amp;MsgID=&lt;MsgID&gt;&amp;Mbx=&lt;Mbx&gt;&amp;realm=bergquistcompany.com</EcpUrl-mt>
<EcpUrl-ret>?rfr=olk&amp;p=organize/retentionpolicytags.slab&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-ret>
<EcpUrl-sms>?rfr=olk&amp;p=sms/textmessaging.slab&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-sms>
<EcpUrl-publish>customize/calendarpublishing.slab?rfr=olk&amp;exsvurl=1&amp;FldID=&lt;FldID&gt;&amp;realm=bergquistcompany.com</EcpUrl-publish>
<EcpUrl-photo>PersonalSettings/EditAccount.aspx?rfr=olk&amp;chgPhoto=1&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-photo>
<EcpUrl-tm>?rfr=olk&amp;ftr=TeamMailbox&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-tm>
<EcpUrl-tmCreating>?rfr=olk&amp;ftr=TeamMailboxCreating&amp;SPUrl=&lt;SPUrl&gt;&amp;Title=&lt;Title&gt;&amp;SPTMAppUrl=&lt;SPTMAppUrl&gt;&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-tmCreating>
<EcpUrl-tmEditing>?rfr=olk&amp;ftr=TeamMailboxEditing&amp;Id=&lt;Id&gt;&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-tmEditing>
<EcpUrl-extinstall>Extension/InstalledExtensions.slab?rfr=olk&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-extinstall>
<ServerExclusiveConnect>off</ServerExclusiveConnect>
</Protocol>
<Protocol>
<Type>EXPR</Type>
<Server>outlook.office365.com</Server>
<ASUrl>https://outlook.office365.com/EWS/Exchange.asmx</ASUrl>
<OOFUrl>https://outlook.office365.com/EWS/Exchange.asmx</OOFUrl>
<OABUrl>https://outlook.office365.com/OAB/bffbef90-82fa-4f63-9994-4b33f4ab4abe/</OABUrl>
<UMUrl>https://outlook.office365.com/EWS/UM2007Legacy.asmx</UMUrl>
<Port>0</Port>
<DirectoryPort>0</DirectoryPort>
<ReferralPort>0</ReferralPort>
<SSL>On</SSL>
<AuthPackage>Basic</AuthPackage>
<CertPrincipalName>msstd:outlook.com</CertPrincipalName>
<EwsUrl>https://outlook.office365.com/EWS/Exchange.asmx</EwsUrl>
<EmwsUrl>https://outlook.office365.com/EWS/Exchange.asmx</EmwsUrl>
<SharingUrl>https://outlook.office365.com/EWS/Exchange.asmx</SharingUrl>
<EcpUrl>https://outlook.office365.com/ecp/</EcpUrl>
<EcpUrl-um>?rfr=olk&amp;p=customize/voicemail.aspx&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-um>
<EcpUrl-aggr>?rfr=olk&amp;p=personalsettings/EmailSubscriptions.slab&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-aggr>
<EcpUrl-mt>PersonalSettings/DeliveryReport.aspx?rfr=olk&amp;exsvurl=1&amp;IsOWA=&lt;IsOWA&gt;&amp;MsgID=&lt;MsgID&gt;&amp;Mbx=&lt;Mbx&gt;&amp;realm=bergquistcompany.com</EcpUrl-mt>
<EcpUrl-ret>?rfr=olk&amp;p=organize/retentionpolicytags.slab&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-ret>
<EcpUrl-sms>?rfr=olk&amp;p=sms/textmessaging.slab&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-sms>
<EcpUrl-publish>customize/calendarpublishing.slab?rfr=olk&amp;exsvurl=1&amp;FldID=&lt;FldID&gt;&amp;realm=bergquistcompany.com</EcpUrl-publish>
<EcpUrl-photo>PersonalSettings/EditAccount.aspx?rfr=olk&amp;chgPhoto=1&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-photo>
<EcpUrl-tm>?rfr=olk&amp;ftr=TeamMailbox&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-tm>
<EcpUrl-tmCreating>?rfr=olk&amp;ftr=TeamMailboxCreating&amp;SPUrl=&lt;SPUrl&gt;&amp;Title=&lt;Title&gt;&amp;SPTMAppUrl=&lt;SPTMAppUrl&gt;&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-tmCreating>
<EcpUrl-tmEditing>?rfr=olk&amp;ftr=TeamMailboxEditing&amp;Id=&lt;Id&gt;&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-tmEditing>
<EcpUrl-extinstall>Extension/InstalledExtensions.slab?rfr=olk&amp;exsvurl=1&amp;realm=bergquistcompany.com</EcpUrl-extinstall>
<ServerExclusiveConnect>on</ServerExclusiveConnect>
<EwsPartnerUrl>https://outlook.office365.com/EWS/Exchange.asmx</EwsPartnerUrl>
<GroupingInformation>BLUPR07</GroupingInformation>
</Protocol>
<Protocol>
<Type>WEB</Type>
<Port>0</Port>
<DirectoryPort>0</DirectoryPort>
<ReferralPort>0</ReferralPort>
<Internal>
<OWAUrl AuthenticationMethod="LiveIdFba">https://outlook.office365.com/owa/</OWAUrl>
<Protocol>
<Type>EXCH</Type>
<ASUrl>https://outlook.office365.com/EWS/Exchange.asmx</ASUrl>
</Protocol>
</Internal>
<External>
<OWAUrl AuthenticationMethod="Fba">https://outlook.office365.com/owa/bergquistcompany.com/</OWAUrl>
<Protocol>
<Type>EXPR</Type>
<ASUrl>https://outlook.office365.com/EWS/Exchange.asmx</ASUrl>
</Protocol>
</External>
</Protocol>
</Account>
</Response>
</Autodiscover>

This may help.  From the exact same machine if I join the northamerica domain I can automatically configure Outlook

If i rejoin it to bqasia domain and try I get the error that there is a problem with the server settings

This leaves me to believe a domain issue?

Probably policy related one, as I mentioned if you have folder redirection for the App Data folder, Outlook 2010 will give you some trouble. Outlook 2013 should work fine.

Unfortunately I need to be on 2010 for the near future.  From what I can tell from the second child domain it is not redirecting to the proper @tbqc.onmicrosoft.com where from the first child domain it is

Thanks for getting me on the right track.  Turns out redirecting was not working so had to modify that child domain so it would redirect online but running the autoconnectivity test helped