You didn't read my post about this, did you? Continuation of CS is NOT a default setting, even in Florida. It has to be specifically ruled that it is in the best interest of the child for the parent-who-is-not-the-parent to continue to help support the child with no right to any other contact.in Florida, if you terminate your rights, you still pay child support because if that were the case, ANYONE could just sign papers and never be heard of again.
If it's not ordered (not just provided as a possibility in the FL statutes) he is NOT required to pay any ongoing child support. The arrearage, however, is a different story as he owes that money from before the date of TPR.