msExchServerSite Value Not Updating

In AD Sites & Services, we have four sites set up...

Site A = 192.168.1.0/24
Site B = 192.168.0.0/24
Site C = 192.168.4.0/24
Default-First-Site-Name, not assigned any subnets.

Sites A & B have two DCs a piece. All DCs are GCs. Site C has one DC which is a GC.

Sites A & B have one Exchange 2013 server a piece. Both servers have the Mailbox and Client Access roles. The Exchange servers were brought into AD before Sites & Services was set up. So their Site and AutoDiscoverSiteScope were originally set to Default-First-Site-Name.

Once we established our sites, we assumed the msExchServerSite value would update automatically based on site affinity. It has not. We have dealt with the issues that result from both servers being assigned to the Default-First-Site-Name for long enough and wish to get this corrected.

How do we get the site affinity to update, and once it does, will we still have to run the command, Set-ClientAccessServer <server name> –AutoDiscoverSiteScope <name of AD Site>, to correct the AutoDiscoverSiteScope?

Some Shell commands below for reference...

[PS] C:\>get-exchangeserver | ft name,site -autosize

Name Site
---- ----
MAIL1 domain.local/Configuration/Sites/Default-First-Site-Name
MAIL2 domain.local/Configuration/Sites/Default-First-Site-Name


[PS] C:\>get-clientaccessserver | ft name,autodiscoversitescope -autosize

Name AutoDiscoverSiteScope
---- ---------------------
MAIL1 {Default-First-Site-Name}
MAIL2 {Default-First-Site-Name}


[PS] C:\>get-adsite

Name HubSiteEnabled
---- --------------
Default-First-Site-Name False
Site A True
Site B False
Site C False


[PS] C:\>nltest /dsgetsite
Default-First-Site-Name