The planets are in orbit, and hence have cyclic patterns. With QBO also cyclical, it turns out it is possible, as your dude does, to choose two planets that simply correlate with the QBO cycle time (in the changing relationship of their distance apart).
This is likely cherry picked correlation. He's picked objects with cyclic behaviour that correlate with QBO. So the first question I would ask is not how does it control QBO, but whether this is a fabricated correlation rather than a causation.
Going from "how is [it] that the orbital perturbations [actually regular cyclic patterns of the distance between two planets] of [two particular, carefully chosen] major planets are seen to directly correlate with with [selected to match oscillations of the] Earths Equatorial zonal winds" to "The question is how does it control the equatorial winds" rather than "what a cute fun random correlation" is a big leap - a presumption of causality.
Most likely you've just found a dude on the internet who has constructed a correlation that has no causality. If that particular pair of orbits hadn't worked out he'd have been able to find a relationship between the rotation of two planets, or something else divided by 3.187 that would do it. And if that didn't do it he'd have found something else that correlated with the North Atlantic Oscillation. Or the Pacific Decadal Oscillation. There are enough cyclical variables out there to find any correlation by relating any two.
You might enjoy reading Nassim Taleb's book "Fooled by Randomness". He points to similar issues at play, with people reading too much into probabilistically random events.
