So, If your Witness is in your primary site, the databases will not mount automatically in the secondary site after a primary site failure.
Why? because in the secondary site you run out of enough votes. My explanation: if you have 2 servers and a FSW then you have 3 votes, if you loose your primary site then you loose 2 of 3 votes and you don't have enough to start the cluster service in the
secondary site.
taking that in care you need to plan how to recover the secondary site to get your databases up and online. This is pretty easy in Exchange 2013 and Exchange 2010 but you have to take in care the following:
1. You have configured the DAG in DAC mode
2. You have created an alternative File Share Witness in the secondary datacenter.
After you are ok with that prerequisites the process to do a failover in a secondary datacenter without enough votes are:
1. Stop-DatabaseAvailabilityGroup DAGNAME -ActiveDirectorySite "LostADSite" -ConfigurationOnly
This needs to be done in the secondary site. If your AD servers and Exchange server are on line in the primary site (maybe for a connectivity issues than lead into a secondary site activation) you need to run this command in the primary site as well.
Important: you can also use the servername switch if you don't have splitted the AD sites. You can't use the -ActiveDirectorySite Switch if you have a single AD Site crossing both physical sites.
2. I always recommend to turn of the Exchange servers in the dead site (primary site in this case). Including the server hosting the File Share Witness if is possible. But is a personal recommendation.
3. be sure that the cluster service in the surviving exchange server is stopped or stop it using the command
Stop Service ClusSvc
4. Run Restore-DatabaseAvailabilityGroup DAGNAME -ActiveDirectorySite "SecondaryADSite"
Important: see point 1 for recommendations
5. In this moment your databases will be starting or already started. If not run again the restore-DatabaseAvailabilityGroup cmdlet or try to start manually the databases using the Mount-Database switch
Hope this helps.
The switchback include the start-DatabaseAvailabilityGroup cmdlet pointing to the primary ADSite or to the server in the primary site.
Also after your secondary site activation, your cluster service will be pointing to the alternative witness instead the primary (even when in Exchange seems to be well configured). To ensure that after recover the primary site everything will work fine the
next time, you need to run the cmdlet Set-DatabaseAvailabilityGroup DAGNAME once again without any other switches. This will reconfigure the DAG settings to their initial state.
If you want to read more, this is a great blog to understand some concepts about HA
http://blogs.technet.com/b/exchange/archive/2011/05/31/exchange-2010-high-availability-misconceptions-addressed.aspx
And also you can use this PPT prepared by the Exchange team in your switchover or failover procedures
http://blogs.technet.com/b/exchange/archive/2012/10/19/exchange-2010-datacenter-switchover-troubleshooter-now-available.aspx