Pierre, two points to note:
1: When passing the traffic information did you tell the pilot the height readout was unverified? We are taught to use "indicating FL*** unverified" when passing such information.
2: Any pilot using TCAS as a sole form of separation when under a RAS is just plain stupid. I have seen pilots inside CAS asking about traffic on TCAS and found that the display showed the a/c about 8 miles out of position. I hope that in your case that the pilot was aware of his actions and that you no longer were responsible for any separation against this conflict. I'd have downgraded the service and passed traffic updates as required and seen how he responded to that too.
Edited as PPRuNe Radar posted at the same time!!
Radar - I think Pierre was a little shocked that this pilot used TCAS as the sole source of traffic avoidance, surely we all know that their accuracy isn't perfect as a radar display so I think a compliance to the Controllers avoidance would have been safer.