I wonder what Tyler was actually told by the center about "talking to Cate." We've seen how Tyler interpreted Teresa's request not to talk about Carly on the show; I think that he was told something slightly different by the Center and has interpreted it in the most passive aggressive way possible (see: repeating that he's not "allowed" to say anything aboutCate).
Cate doesn't get a totally pass from me either. She needs to do the work to get better. Maybe she's refusing to really make the changes as a way to stick it to Tyler. I've been in the death throes of a significant relationship and the petty shit that we both did rather than just pulling the plug is still embarrassing many years later, so I can get where Cate is coming from.