GoldSpark said:
When he is on top of some AABB all I do is change his Y position to that AABB's position.y + size.y so the character stays on top and his Y velocity to 0.

Does not sound wrong, although you may want to use a min instead setting, so the character can still move away from the platform, and only penetration is resolved but not separation. But that's unlikely the cause of your issue.

Eventually that's the reason: After the collision is resolved, gravity will pull the character down again, causing penetration again. If you render the character using that position, it will penetrate. And if your timestep isn't constant, penetration depth also isn't constant, causing jitter. See https://gafferongames.com/post/fix_your_timestep/​

Otherwise i propose to log things like collision happening or not, positons before and after resolve, penetration and timestep for each update​, which should help to find / understand the true reason.