Local vs online TMs

I have yet to give Trados Live a try and I may be out to lunch on this, but am I right to say that once I create online TMs by importing my existing local TMs and start using them in online projects, my offline TMs won't be kept in sync? I realize I may be asking a stupid question, but if you're working both online and offline, how do you go about making sure the TMs you're using are as up to date as they can be?