I’ve always found electricity incomprehensible, I got about 30 seconds into that Lionel video....
so, if I understand this correctly, the transformers will be in phase, or 180 deg apart; there are no other possibilities. I can determine this by wiring up the two lines (because the thumbscrew terminals on the controller outputs, are the easiest place to change wires) setting the controllers to 60% or so, connecting the BLACK terminals on the two controllers, and brush the ends of the RED wires together.
If no spark, no action is required.
That should work, but as Rich said, it’s better to have all in phase. If your transformers are all modern and of the same make, they probably are. Be good to know what the 220/110 and 110/20 transformers are, what the plug the that goes into the wall socket looks like and what the interconnecting wires look like.
The controller set appears to be MTH 40-750C with a Z-750 controller. Those are rated at 75 watts so if your transformers are rated for at least 150 watts, you could run both Z-750s from one 220/110 and 110/20 transformer pair and not worry about phasing them.