I have had the same problems before. For a great period of time I could not play passage work (scales, etc.) fast because of tension and pain in my rest. Although I don't completely understand what your teacher is looking for, I would recommend a different approach from the others. If you think of a "finger" staccato, you'll probably continue to be tense. The majority of motions used to play involve your entire body, not just your fingers, or your back. I would begin by first dropping your fingers into keys, one at a time. Once you have landed, focus on relieving the tension. This doesn't mean you have to move, but you might be "bearing down" on the keys, a term my teacher uses. Anyway, I would begin with that. Also, ask your teacher about the problem. If it's been persisting, he/she probably should have noticed it in your playing, and if they haven't you might want to find a new teacher (it's hard, but I had to also). Finally, I would also consult your doctor is it doesn't got away after all these different approaches. For awhile I thought that I was just fine, and it turned out that I hard tendonitis.
Anyway, good luck. :-)
Mike