Cross Database transactions with Availability Groups
The article isn't well worded but here's what I think it's saying

Beginning scenario - DatabaseA is in an AG and is currently primary on Server1 and can run on Server2.  DatabaseB can only run on Server1

T1 - Transaction begins
T2 - Row inserted into DatabaseA (log not yet sent to Server2 though)
T3 - Row inserted into DatabaseB
T4 - Transaction commit called
T5 - DatabaseB commits transaction (since the two DBs commit individually)
T6 - DatabaseA fails over before log is sent

Since the log was never sent DatabaseA wouldn't have the row but DatabaseB would.  If synchronous mode is being used that can't happen because the commit can't be called until the log from the row is sent.  However, it may be possible for the commit on DatabaseB to happen and DatabaseA to fail over before the commit happens there.  This may lead to a rollback in DatabaseA instead of a commit.  I can't say with certainly that you can get into the same situation with synchronous mode but if you can that's how it would likely happen.