TCAS is the safety net. If it generates a resolution advisory, that indicates that the air traffic control system has failed, (or there has been a level bust) and therefore it is common sense, and SOP to promptly obey the RA regardless of what ATC has instructed. As soon as time permits, the crew should communicate that fact to ATC, using the phraseology "...TCAS climb/descent".
Under these circumstances, a good ATC should instruct you : (...TCAS is priority, descend FL...)
Incorrect. Under these circumstances the ATC should do nothing, except advise the location of any known essential traffic, and plan any recovery strategy that may be necessary. ATC should not interfere in any RA generated, even to pass a recommendation to follow it.
In the case of the TU154/B757 event, the controller was unaware that at the time he became aware of the impending loss of separation and took steps to resolve that, that the TCAS of both aircraft was about to command a different response. That the crew of the TU154 elected to follow the ATC instruction was, regrettably, the final link in the chain.
The controller had no way of knowing the TCAS had generated an RA.
There is still no automatic feature in the ATC system (that I know of) that provides this information to the controller. If any of us become aware of a potential conflict/loss of separation, we will take all steps to prevent a collision and restore the appropriate required spacing. It is not only in our nature to do this; it is a requirement. Right up to the time one of the crew informs ATC they are responding to a TCAS event.