The lodestone suggests you're now the master of the FC (either because you were before or due to inactivity it switched to most active person ie you).

So him logging in shouldn't make any difference... Maybe worth checking you actually have a valid email address in your square enix account might be why no emails (or they're in junk folder?) but from what you've said sounds like demolishing should stop but I appreciate that's not very reassuring and you want to know for sure.

Walking into the house is all that anyone needs to do though