I assume that will be explained. But I get the feeling he has been involved as soon as El opened the gate in s1. I think the demogorgon, the Mind Flayer, demodogs, etc were all weapons he was using to try to kill El, but since they all failed he finally decided to take matters into his own hands. Now he's opening more portals to make his connection to our dimension stronger so he's more difficult to defeat. If that's the case, Dustin's theory about him being the Mind Flayer's 5-star general is wrong. It makes more sense to me that Vecna would be the man behind it all since he has personal motives and is a better vessel for communicating that to audiences than a giant smoke monster thing.
However, the Upside Down likely existed long before Vecna arrived there, so maybe he is just a pawn of the Mind Flayer?