While that is a fair point, I can't imagine it being in the best interest of a death cult styling themself after the Eversors to show allegiance to someone like Zophar. Especially not if they're a cult in which the Eversor temple show special interest. What if they're found out? The Eversor temple are not a group you would want to have personally angry at you. Even if they didn't retaliate themselves, you'd at the very least become a target for either the Hereticus or Sicarius. After all, a Death Cult which is rabidly loyal to the Imperium is a very tolerable thing, one which has been seen to allign itself to Chaos is a very dangerous thing. And having one of your members 'do the dirty work' for a heretic is a very good way to be caught. 'Hey, doesn't that guy on the vid feed killing everyone look exactly like a member of the sanctioned Death Cult X...' (the Eversor temple are not exactly un-distinctive and neither would a member of a cult who dress to look like the Eversor temple).
To be honest, I find that entire plot to be more contrived than simply 'There was a member of Death Cult X (i haven't thought of a name yet), he was seduced by Chaos, which Sarthuul introduced him to. He decided to escape his own Death Cult to join Zophar and perhaps pursue the benefits which Chaos can bring'. That, to me, seems fairly reasonable, credible and straightforward.
While I disagree, I still appreciate your input. I think I simply have a different vision of this character's fluff.