I think the game mechanics answer to this is going to be related to the mechanics for Truestone. The canonical Gloranthan answer is, of course, that they don't get this power.
Except that some rune spells are one use, and use up Rune Points permanently, while others are reusable, and you can only use the Rune Points with a specific cult to cast spells from that cult - you can't use your Eurmal RP to cast a Heal Wound that you got from Orlanth.
But going with that idea, if an Atyar cultist drains an Ernaldan and casts Charisma with their Atyar RP, they can regain the RP. If they cast Gnome to Gargoyle, do they lose the Atyar RP permanently, since Ernalda only gets it one-use? I think the link between the spell being reusable and the loss of the cult RP is an important one, and it doesn't make much sense to me to muddle the two. I can't think of a good compromise though, and I don't have access to the Atyar cult writeup to see what Consume Mind says.