Speculation aside, what we know through their own words is that White's defense became more multiple to accommodate Rhule & staff's preferences vs various opponents. We know the coverage went from a base man off to quarters & the formation was much more commonly a static 4-2-5. I wouldn't describe any of these changes as more conservative, but you are naturally blitzing out of the 3-3-5 on virtually every play.
Did they clash? Did Rhule want a more conservative defense? I wouldn't pretend to know. But, the fact White is moving laterally suggests there was probably too many chefs in the kitchen for his liking.