So for starters, Izuku is still the one with the ghost quirk in this AU; Hitomi’s quirk is empathy and emotional amplification. Because of this, Izuku ends up with a much stronger and potentially tangible ghost than normal; it’s really only his young age and memory problems that keep him from fully tapping into his postmortem potential. If anything, this gives him the capacity to be even stronger than Rei Classic, freaky screaming and face-melting included. On the other hand, he lacks Rei Classic’s temper and possessiveness, so he’s a lot slower to get angry and try to claw someone’s eyes out.
This sort of renders poltergeists a mute point for Hitomi; since Izuku’s still the one with the ghost sight/enhancing quirk, other ghosts and poltergeists can’t affect Hitomi unless he specifically brings them to her. She can perceive them to a certain extent thanks to her empathy, but she can’t see or hear them, and they can’t hurt her the way they can hurt Izuku.
Ghost Izuku often ends up running to Hitomi when he meets a scary ghost. She gets it, though, and she’ll let him cling until he calms down.