I've recently re-watched the second episode, the one with the Imposter Demon, and I don't think that Harry was referring the demon as having the magical power to manipulate emotions, only that it had a (mundane skill) to manipulate people's emotions.
The quote that I think is relevant: You [the charmed ones] are not the first to fall for an Imposter Demon. Let's just say I'm pretty sure that's how brexit happened. They [imposter demons] are considered lower-level demons because their real power is emotional manipulation. And in some ways, that makes them the most lethal...
I think that Harry was merely saying that the imposter demons were magically weak and they simply resorted to psychology, rather than raw power, to get what they want.