Now, I have some issues with the Demon Lords, namely I think they're far too weak outside of their realm, but recently someone read the rules text a little bit differently than I did.
The line in question:
A demon lord gains the following additional powers while in its realm:
Mythic: A demon lord functions as a 10th Mythic Rank creature, including the Mythic Power ability (10/day, Surge +1d12). It may expend uses of Mythic Power to use the Mythic versions of any spell-like ability denoted with an asterisk (*) just as if the ability were a Mythic spell.
Now, the way that I read that was just that they simply qualify as Mythic for targeting purposes while within their domain and gained Mythic Power for Surging and Mythic SLAs.
The way the other person read it is that each Demon Lord becomes a fully functional mythic creature that must be statted up by the GM for their own realm, gaining 100 extra HP, 11 mythic abilities, 5 mythic feats, etc. All of which would *officially* raise each Demon Lord's CR by 5 when within their realm (which as I think we all know at this point, treating 2 mythic ranks/tiers as CR +1 is just laughable, but that's beside the point)
So who's correct?
You are. The rules are talking about Mythic Ranks, which are a quick and dirty way to give monsters mythic power. The other person is talking about Mythic Tiers, which players (and select NPCs) use to get lots of customizable and potentially more powerful abilities.
It's a fair point that the CR for these guys should be different at home vs. away.