Broadly speaking, a TCAS system acts like an ATC ground station... The TCAS antennae transmit ATC-like interrogation signals and the other(intruder) aircraft respond via their ATC systems, giving, hopefully, altitude information. The other(intruder) aircraft's ATC systems get their altitude(29.92) information from their ADC's or ADIRU's. In your scenario, you are the intruder.
When two TCAS-equipped aircraft are about to collide, the airplanes talk to each other via their ATC systems to co-ordinate avoidance manoeuvres.
Hope this makes sense.
Rgds.
NSEU