My feeling is that that describes to me either a bike setup error, or an incorrect body position. I see this sort of positional error all the time with skating, and it's just because people's own proprioception and body self knowledge has a very different feeling to what they see in others demonstrating the correct position. It's very hard to adjust this sort of thing, and it takes a lot of disciplined care and persistance. I've noticed the same sort of thing watching cyclists - watching body language and movement is my full time job after all, I can't just turn my eye for it off.
Core strength may patch the symptoms, but it won't address the cause of discomfort.