Ben was seduced BEFORE he began Jedi training

A master of the Force and a seeker of arcane lore, Snoke seduced young Ben Solo when the Force-sensitive boy desperately needed a teacher. Snoke’s influence would prove critical when Luke Skywalker finally agreed to make Ben one of his new Jedi apprentices. Ben destroyed Luke’s temple, left with several of his students, and slaughtered the rest. Snoke then became his new master.

-- starwars.com databanks

That's pretty dope. I like it.

Snoke didn't become Supreme Leader until after Kylo's fall:

Snoke’s plans were coming to fruition. He rose to become Supreme Leader of the hermetic First Order, which was building a mighty war machine beyond the veil of the galactic frontier. With this military buildup complete, Snoke agreed to decapitate the New Republic by incinerating the Hosnian system and the Senate, and sought to find Luke’s place of exile and kill the last Jedi.

Hm, well that's interesting. Although doesn't this kinda contradict some of the other material? Cause those seem to imply he was Luke's student for a time before all that, not immediately.