Not exactly.
"traffic, traffic" is a TA, not an RA.
In the scenario given, monitor V/S will not be issued before adjusting, because we are the aircraft causing conflict. Monitor V/S is instruction to keep present rate, which is exactly what we must not do and TCAS will advise accordingly.
I also do not recall any "reduce descend" alerts but my manual thinks differently
2 out of 7 aircraft apparently have an older version of software that has "reduce climb, reduce climb" and "reduce descent, reduce descent" alerts. On later models, these are replaced by "adjust vertical speed, adjust".
FD
(the un-real)
Oh, just to pick a nit, the difference between TA and RA is not closure rate dependant. It is distance dependant. This way the system keeps you from crashing into somebody gently.
In other words, FMC Ovht: You are correct. What brings you such a question?