I've never read of any loyalists jumping ship after the Heresy began.
Horus recruited every Primarch to his side he could before the killing started on Istavaan III .
That was the whole point of that trap, to kill everyone he knew would never join him. If Horus couldn't sway a Primarch to his cause, that Primarch's Astartes would certainly not join him.
Once the Heresy began, Horus was planning on wiping out every single loyalist marine in the galaxy in one fell swoop. Coupled with the events of Istavaan II, he sent the Word Bearers to ambush / exterminate the Ultramarines and I'm not sure about the White Scars but I'm sure he had plans for them too. All in all, Horus was a bit of a dick.