You might not want to use missile troops to push towers, the towers have their own artillery, and I think you can't use it if the unit pushing it is a missile unit. This might also apply to units like hastati, not sure. See this thread:
https://forums.totalwar.org/vb/showthread.php?t=40510

If you want reinforments to be somewhat useful, do not have a general in the reinforcement stack, this gives you control over the stack's units when they arrive. If there is a general in the stack, he controls the stack, and will usually get himself and a lot of his men killed.