To move engines to active, you must first tap Edit. If DCS engines, they won't move if not powered, just as with the remote. TMCC/Legacy engines don't need to be powered since they can't be seen at all.
TMCC engines don't show up and don't with the remote, either. They always must be manually entered to be available.
If you built a lashup but couldn't find it in the engine roster, you didn't complete building it.