I've been giving cultists the same stats as cthonians, but with the special attack activated by the moon dimensional symbol. Is that what everyone else is doing?

 I've played them as exactly as being Cthonians, symbol, etc

I assume "stats" means everything, including its symbol and movement color. Treat it as though it's another Chthonian token: no more, no less.

I was also searching the forum for a response on this question and a little more.

But firstly I've been using the stats of a Cthonian but activating those stats on the moon symbol.

The next part I was querying was those monsters that are 'treated as cultists' are they by being treated as Cultists therefore also treated as Cthonians?

I have found this chapter to be a shocker. I managed to draw the terrible experiment as the 2nd Mythos the other night and given that I played any monster who is treated as a cultist as a Cthonian I ended up with 4 monsters arriving as the result of the rumor not being resolved.  4 rolls of the die and not one 1 amongst them 4 losses of stamina on each investigator they all ended in St Mary's. Next upkeep phase rolled to see if two of the investigators retained their blessing - guess what two 1's  the game was meant to be over quickly

Just realised didn't remove BGOTW monsters - no wonder I've been getting wiped out by those monsters that are treated as cultists plus a few other nasties.