When a TCAS RA is issued, the system first selects the sense (up or down) and then the required strength. During the sense decision, an altitude crossing is avoided if the required vertical separation is sufficient:
The first step is to select the sense (upward or downward avoidance) of the RA. Using
the results of the vertical and horizontal tracking, the logic models the intruder’s path to the CPA.
CAS logic computes the predicted vertical separation for each of the two cases and normally selects the
sense, which provides the greater vertical distance.
In the cases where an altitude crossing is projected before the CPA, the CAS logic will pick the sense that
avoids crossing, provided that the resulting vertical distance at CPA is sufficient.
Figure 19 illustrates this case. The desired amount of vertical safe distance (ALIM), varies from 300 to
700 feet, depending on own aircraft’s altitude regime. If ALIM cannot be achieved, a crossing RA will be
issued (see Figure 20). However, delaying mechanisms aim at reducing the incidence of crossing RAs by
deferring an altitude crossing advisory if:
- one aircraft is level, or when the two aircraft have vertical rates in opposite senses and they are
separated by at least 600 feet; or
- when both aircraft have a vertical rate in the same sense and they are separated by at least 850 feet.
A resolution advisory is altitude crossing if own ACAS aircraft is currently at least 100 feet below or above
the threat aircraft for upward or downward sense advisories, respectively.
(Eurocontrol - ACAS Guide - Airborne Collision Avoidance, emphasis mine)
Figure 20 illustrates the case where the separation for non-crossing (vertical distance at B) is below the minimum desired value (illustrated by the black arrow). In that case, a crossing RA will be issued with "Descend, crossing descend; descend, crossing descend".
You also asked:
Furthermore, how can the TCAS system presume that descending/climbing aircraft will maintain its rate of descent/climb?
The TCAS will always presume that the intruder maintains their current flight profile. This works if the other aircraft does not have TCAS or if the other aircraft is maneuvering such that the vertical separation is even increased.
For crossing RAs, this can however result in a situation, where the other aircraft maneuvers such that the vertical separation is reduced. This will then trigger a modified RA:
During the course of the encounter, the RA strength is evaluated every second. Occasionally, the threat
aircraft will manoeuvre vertically in a manner that thwarts the effectiveness of the issued RA. In these
cases, the initial RA will be modified to either increase the strength or reverse the sense of the initial RA
(when the initially issued RA is no longer predicted to provide sufficient vertical spacing).
[...] Figure 23 shows an encounter where an
initial Climb RA requires reversal to a Descend RA after the threat aircraft manoeuvres.
(Eurocontrol - ACAS Guide - Airborne Collision Avoidance)