I suppose what it is would depent on whether its a genuine medicine needed to combat some side effects from their witch modifications or purely a method to control them. If the former, it could be anything, like David's vitamin K, but if it's the latter, logic would dictate it's something a bit more complicated so that escapees wouldn't be able to acquire it easily, for example an enzyme.

I fully agree on the main character dude's power coming out of nowhere and for no particular reason. It would have been at least partially remedied if it had been used in the beginning: For example saying the dude was bullied as a kid because of his unnatural memory and Neko was his only friend because of that.