This happens from time to time in my neck of the woods.
Simple (and I believe most likely) answer: The aircraft at 4500 FT had a faulty altitude encoder/mode c. The aircraft was at 4500FT, the transponder (not its tcas - it mayy not even have had tcas) - was mis-reporting the altitude.
Simple answer, when the actual altitude differs by more than the allowed tolerance, is to get the offending a/c to de-select mode C.
To answer your questions, in order:
1) "Is it smart to ask a pilot to turn off his tcas when something like that happens?"
Not appropriate, as it is the transponder that is faulty.
And no, it is never smart to get a pilot to turn off his tcas. In most cases the pilot would/should decline to do so.
2) "What's the best way to deal with this situation? (besides providing vertical separation)"
See above. The offending a/c should stop squawking charlie.
3) "Why do you think only our secondary radar (eurocat) plus 1 out of 3 aircraft saw this ghost target while two primary radars (clark's seles and Mnl app's thales) saw the target as it really was?"
Your radar was probably correctly displaying what was input to it. The other (primary) radars would have no way of reading the transponder signal, and would be reporting the (approximate) correct altitude of 4500FT, based on their slant ability/triangulation.
The other aircraft that saw the FL183 readout saw on its TCAS what was being signaled by the faulty transponder. The aircraft that did not record/report that were most likely far enough away in altitude or range that the signal did not trigger any kind of advisory. Can't really be sure of that without being there and seeing what you were seeing.
3.1 "what do you think is common between my radar and the 3rd aircraft's tcas?"
They both indicated the information that was transmitted to them. Chances are, your Eurocat gear is fine. The VFR a/c concerned needs to get its transponder fixed.
Hope that helps.