For some reason, Ostia’s pulse doesn’t seem to be working for me. If I’m not mistaken, it’s supposed to shorten the cooldown count of you special by 1 at the beginning of the level, right? That’s not happening, and I do meet the movement requirement. (He’s on an armor team)
The problem is that his Special only works on Mixed Emblem teams. You can have a max of two units of the same Move type if you want to take advantage of Ostia's Pulse.
I fear you don't meet the requirement for Ostia's pulse, you must NOT have more than 2 ally with the same movement type in the team (same as def/res/atk/spd tactic). An armor emblem have 4 unit with same movement type, so Ostia's pulse don't work
It's actually a very common misinterpretation related to tactic skills; I made the mistake myself for the first month or two of my play. It's easy to misinterpret and I wouldn't think anyone unintelligent over this misunderstanding.