Yep, use the fine tuners.
Sometimes a locking trem will go slightly flat (usually all the strings, or at least half by a few cents)... a cool trick in that instance is to very slightly screw in the claw on the affected side, or both sides if necessary to bring the guitar back in tune. Just make sure to depress the trem before doing this and after each slight adjustment to make sure the springs aren't fooling you with stored slack.
You can always unlock and tune for 5 or 10 minutes to do this, but you accomplish the exact same thing by using the
claw screws while everything is locked... the adjustment is so slight there is no noticeable change in the float. Otherwise, if the guitar is unusually flat or sharp you'd need to unlock and tune formally, anyway.
Double
locking trems can be a pain if you let them, but once you understand how they work you can slap them around like cheap hos and make 'em work for you.
RR