In your application, the electrical signal propagation through wires is practically instantaneous. You don't have to worry about it at all.
Propagation through everything else but the wires, though, is another story - and that's where control theory and feedback circuit design comes into play. Typically you shape the frequency response of various parts of the circuit so that the control loop remains stable.
Well, I basically thought (wrongly) that each "loop of the current" in my circuit would contain many periods. So changing the phase every xx periods would have worked as I wanted (I thought to vary the command of a buck converter from a state to another accordingly to that information of phase, with that variation damped by a low pass filter
You seem to think that the only way to store state in an electric circuit is by having a long wire that propagates state. In your case this would be a serious limitation and require extremely long wires :)
Instead of storing state in a wire, it can be stored in a low-pass filter directly! The filter - even the simplest first order R-C filter - imposes its own response on how the signals propagate through it.