Yes, you still have to pay fire control tonnage. Anti-missile systems are classed as heavy weapons and explicitly follow the core construction rules for all purposes other than gunner requirements (TechManual page 204). In addition, if you look at the weapons charts beginning on TechManual page 341, you will find that AMS is noted as requiring a slot on DropShips just like weapons do. The same rules apply to JumpShips, WarShips, and space stations.