I am not that well-versed on rothschildianum, by itself, but the best time to repot any plant is just as new roots are emerging, which usually coincides with new growths in paphs. Tying it specifically to a season might be a decent generalization, but not a particularly reliable one.
As roots grow, their cellular structure becomes optimized for functioning in that environment. Once they have grown, they cannot change. Move those roots into a different environment - a new potting medium or even a fresh version of the current, broken-down one - and the existing roots are immediately sub-optimal, so will begin to fail, with the rate determined by just how different the "new" and "old" pot conditions are.
If the plant is actively growing new roots, they will grow optimized for the new conditions and support the plant while the old ones go away.
If, however, you really need to repot at the "wrong" time, or you risk losing the plant altogether, by all means do so, but just keep the plant in moderate temperatures, high humidity (to slow transpirational losses) and shady - i.e., "super comfortable" - and it'll recover fine. Treating it with a biostimulant like Kelpak certainly helps.
That all said, in my experience, most paphs seem to go into a growth spurt after repotting, and it doesn't seem to matter much when that is done.