A321 Captain reported an NMAC during visual approach with a Citation that was on approach to a different runway. The Citation flight crew took evasive action.

Narrative

Had a near miss with a Citation with separation of 200 feet and less than 1/4 mile. Event occurred while on the RNAV Visual Rwy XX. After passing ZZZZZ; ATC informed us that we had Citation traffic at 4 o'clock and that the Citation was on the visual approach for Rwy XY. We looked; but did not locate the Citation. We were told that the Citation had us in sight and would maintain visual separation. I figured that the Citation would pass behind us while he lined up for Rwy XY and we proceeded to Rwy XX on the charted RNAV Visual. We had now passed ZZZZZ1 flying towards ZZZZZ2. I commented to the First Officer (FO) about how low to the ground this approach brings you in. (which I believe disables the RA descend feature of TCAS). ATC did not issue a traffic alert. The only moment I knew there was a traffic conflict was when the TA oral said 'traffic' and the screen showed the aircraft 200ft above and what appeared to be right on top of us. We looked to the right and saw the bottom of the Citation doing a climbing right turn. I do not know what prompted him to do this aggressive maneuver; but had he not done so I believe he would have hit us.There are a few factors that contributed to this event. The primary being that when another aircraft says they will maintain visual separation I relied on that pilot actually doing so. The other was a factor of safety features of the TCAS system working against us. I can understand why the system doesn't issue a descending RA close to the ground; but that is really what we needed to do to increase the separation from the approaching aircraft. A turn was not an option and a climb would have caused a collision. The third casual factor was my reliance on TCAS to issue an RA. When the TA showed an aircraft so close and only 200 feet above me; I should have instantly disconnected the autopilot and descended the aircraft even though we were already low to the ground.Being more proactive locating traffic even when the other aircraft reports that he has me in sight. In addition; not relying on automation to command evasive actions. Even though I was only between 1500-1700 feet AGL when the event occurred; I could have descended the aircraft to 700 AGL immediately.