Restoring a SQL Server 2012 database in high availability
Listen to your adviser.  By restoring a backup, you are essentially replacing the database schema and data.  You will need to turn synchronization off, remove the DB from HA and perform the restore on the primary and replica, leaving the replica version in a restoring state by using WITH NORECOVERY.  Once your backup is in place, put the DB back into HA and start synchronization again.

HA is very similar to mirroring and uses similar technology, just not nearly as finicky.  You will want to treat your HA DBs similarly as well.

Code would be similar to the following:

--on primary

ALTER AVAILABILITY GROUP MyAG REMOVE DATABASE AdventureWorks2012;


--on primary

RESTORE DATABASE AdventureWorks2012
   FROM AdventureWorksBackups
   WITH NORECOVERY, 
      MOVE 'AdventureWorks2012_Data' TO 
'C:\Program Files\Microsoft SQL Server\MSSQL12.MSSQLSERVER\MSSQL\Data\NewAdvWorks.mdf', 
      MOVE 'AdventureWorks2012_Log' 
TO 'C:\Program Files\Microsoft SQL Server\MSSQL12.MSSQLSERVER\MSSQL\Data\NewAdvWorks.

RESTORE LOG AdventureWorks2012
   FROM AdventureWorksBackups
   WITH RECOVERY;


--on secondary

RESTORE DATABASE AdventureWorks2012
   FROM AdventureWorksBackups
   WITH NORECOVERY, 
      MOVE 'AdventureWorks2012_Data' TO 
'C:\Program Files\Microsoft SQL Server\MSSQL12.MSSQLSERVER\MSSQL\Data\NewAdvWorks.mdf', 
      MOVE 'AdventureWorks2012_Log' 
TO 'C:\Program Files\Microsoft SQL Server\MSSQL12.MSSQLSERVER\MSSQL\Data\NewAdvWorks.ldf';

RESTORE LOG AdventureWorks2012
   FROM AdventureWorksBackups
   WITH NORECOVERY;


--on primary

ALTER AVAILABILITY GROUP MyAG ADD DATABASE AdventureWorks2012;


--on secondary

ALTER DATABASE AdventureWorks2012 SET HADR AVAILABILITY GROUP = MyAG;