When our cert expired, how come domain users were able to connect but non-domain users were not?

We have some users in a domain and some users not on the domain. The datacenter is a remote location from all user sites.  When our certificate expired last week, people who are on the domain using NTLM are able to connect without any problems; however others not on the domain were not able to connect before we renewed the cert.  Any thoughts on why this is?  Do people using a domain profile connect differently to exchange?  Everyone should have been connecting via RPC over HTTP/s.

I'm certainly no expert in exchange, but trying to learn.  Any insight would be appreciated.
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Where the certificate "installed" on your domain computer and not on the other computers?
instaITAuthor Commented:
Root cert and intermediate cert authority are both installed on all computers the same.

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