Yup been there too.
In fact it got so bad that we would dread being anywhere there were reflections as Dad would yell at the reflections at the top of his voice no matter where we were.
You never realise how much we are surrounded by reflections...walking past car windows you get reflections, walking past shops you get reflections, staying in hotels we'd have to cover the mirrors, at the hospital we had to drape a sheet over the full size mirror in the toilet...
I think part of the problem was because his reflection always looked angry or confused...so he assumed it was a 'bad man' (his words).
Now tho, I'm not sure he knows its him again, but he doesn't seem as concerned but he definetly is always curious about that other man.
Something that has helped for us, is to touch Dad on the face while he is looking at the reflection and by doing so this shows him it is his reflection i think, in that he feels the touch on the nose and sees the reflection getting touched on the nose at the same time...What always worked for me was to explain to Dad that he was just seeing a reflection...in a very calm voice, not making it sound like he was stupid or crazy...just saying to him 'Remember Dad that is your reflection, remember you have trouble recognising reflections now, see its a reflection because there am I (point to my nose so my reflection does too) and thats your reflection (touch him on the nose)'. I didn't work if I just pointed to the reflection, it only worked if I touched him and said it.
Don't know if that will work for you...but you never know...
Otherwise the trick is to get quick at anticipating reflections that they might see and distracting them from it before they noticed it.
Good luck.