Normally, the protected areas are staggered so that an intruder crosses the yellow TA area first before he has a chance to enter the red RA area.
Here is a FAA-provided introductory pdf, in case You are interested.
If a resolution advisory is generated, it is to be followed within 5 seconds. Airbus has provided memory items for that case that have been changed a little bit with the advent of Auto-TCAS, find them in OM-B - PRO - ABN - SURV - [MEM] TCAS WARNING - RESOLUTION ADVISORY.
In a nutshell - if the auto TCAS works as intended and as required, that is fine and acceptable. But if it does not, it is the classic memory item that has been around for ages. Autopilot/Flight Director off (to achieve SPEED or MACH in the FMA), then fly the required vertical speed and have the PM announce the RA to ATC. Or, with a CLIMB RA in final approach in Config 3 or Full - go around.
Overreliance on the automatics has often caused a headache lateron...