Easy, Because Jet and ACE have no problem sharing an Access BE on a LAN and controlling whose update prevails. If Jet and ACE (Access has actually nothing to do with this) couldn't control serializing updates, they would be pretty poor database engines and would have died years ago. Also, the op kept talking about synchronizing and that is simply not something that happens when sharing a BE on the LAN. There is only ONE data source and that is the shared BE on the LAN. There is no reason to synchronize anything.
If your processes are updating multiple tables and all updates must be completed or all must be rolled back, you can put Access into what is commonly called a "deadly embrace" if your processes don't always lock the tables in the same order. Short of that, Access, left to its own devices - optimistic locking - does not attempt lock a record until the user goes to save it. The conflict occurs if two users read the same record and both try to update it. The first user to submit the update, achieves the lock regardless of who read the record first and his data gets saved. Other users, will get a confusing error message with three options when/if they try to save. There are other locking options. The one that control freaks love is "pessimistic" locking. That method locks the record when the user reads it. Yep, that sure solves the problem as userA reads a record and heads out for a two hour lunch locking up the record and keeping everyone else out.