Your TCAS will also be fooled!
Wrong. Safely ignore anything this guy says.
By the nature of the question, you are in the US, chinny? Follow whatever your company SOP states. In the absence of an SOP, follow the advice taken from the AIP (above). You
should change at the transition layer/level- however, human factors have dictated some common sense be applied (hence the AIP procedure).
This is a forum with international following, so rules will naturally vary from location to location. The mechanics of TCAS doesn't.