
Something about them had been changing since Ja-heon arrived. There's been a couple of times where Mugo has commented on it. For instance, when Monster Mugo stayed in control during sexual moments where it should have switched to Jerk Mugo. They even say last chapter "You instigated some sort of change. I need you." There was during the rut too where Ja-heon could swear that all 3 Mugos were there. Something is changing their chemistry and I think this is fully the intention of Mystery Mugo who we now know is the one who told Ja-heon to bring sweets so he'd survive.

So each Mugo serves an important purpose/identity. Sir Mugo is the one who sees themselves as a Guardian Deity of the family. Monster Mugo likely derives from a time when Mugo was starved before he was a Good and is therefore always hungry. Jerk Mugo has a connection to sexual desires. Mystery Mugo is more unknown, but maybe holds his memories?
If you go back to the first chapter flashback, Ja-heon is called out by a Mugo. The text is mostly red when he calls him out (a bit ominous). When he finds Mugo we actually don't get much of a clear view of him, and remember all Mugos have the same face, so Mystery Mugo likely took over during this part. He told Ja-heon to bring sweets. Sir Mugo never confirms that he told Ja-heon to do that.
Sir Mugo sees himself as a Guardian Deity and therefore wants to protect a sacrifice to fall in line with that ideal. He also likely feels an attachment to Ja-heon as well since they are all Mugo and they all like Ja-heon. He never is out when a sacrifice shows up normally so this was his one chance. He took the opportunity that Mystery Mugo set up and gave him the protection spell hoping to have Ja-heon leave and live a normal life. Sir Mugo is their God identity and the others do not follow the way a God acts. The God of the Well even says so; that he's not a real God and the other two Mugos see themselves as more as a Curse and not a God.
ok so there's four Mugo's. Sir Mugo, the "kind" one, Lord Mugo, the more cruel one, and Beast Mugo, who's more childish. And now, a mysterious Mugo, who is implied to have been the one to tell Jaheon to bring something sweet
but like
wasn't that sir Mugo?? like, that's the whole reason he put that protection spell over him right? I'm confused. Did I miss something lol