I do not have TIR, but I have run Exploerer ++ for quite a few years now. The main issue I've experienced with it, is that I can't copy a file in Explorer ++ and then paste it in a Windows Explorer window. Drag and drop doesn't work either, IIRC. This mostly seems to be a Windows issue, though, since every other program I've tried (other file managers, archive managers, etc) all handle these operations with Explorer ++ just fine.
Does TIR work when started via plain Windows Explorer?