Citation Pilot reported on visual approach the Tower issued VFR traffic; resulting in taking evasive action to avoid a collision.

Narrative

We were flying into ZZZ. Once we switch from approach and cleared for the visual to ZZZ tower; tower advised us Aircraft Y had just departed ZZZ1 and was on a westerly heading. Crew was searching for aircraft; unsure of type; altitude and distance. Pilot flying spotted aircraft after pilot monitoring called traffic out and alerted tower the aircraft was in sight. Shortly after Tower gave us the advisory the aircraft; can't recall tail number; but appeared to be an experimental type aircraft. I confirmed with PNF I had him as well. Aircraft Y also confirmed he had us in sight and was instructed to clear from the extended centerline; he acknowledged. TCAS alerted of traffic and I prepared to follow possible RA guidance. We were on a visual approach; all crew members of two aircraft involved stated we had each other in sight. But I prepped for maneuvering because I was truly unsure of his intentions. The typical approach airspeed for this aircraft is 140KIAS and we were doing such; so we passed him with perhaps 200-300' in both vertical and horizontal directions; my best estimation. After we passed Aircraft Y I remember looking back at the aircraft and he had started in what appeared to be a 45-60 degree bank as if he was following behind us. It was strange. Pilot not flying kept constant visual while I flew the airplane and eventually landed at ZZZ. Just prior to receiving the RA I had turned off the autopilot to hand fly the remainder of the approach but the RA commanded the aircraft to do what I was already doing and that was descend. After an uneventful landing and taxi off ZZZ ground queried us and asked if I would give them a call and relay what we saw; encountered and more or less get our point of view. We spoke shortly and the person I spoke with stated that tower controller wanted him to turn east and not cross the extended centerline. Looking back I remember the controller telling the pilot that and he further stated the should not be turning west out of there in south flow due to ZZZ being busy as is. In my opinion it was a close call that was easy preventable with some sort of mandatory left traffic or left turn out from ZZZ1 when in south flow. ZZZ is busy with airplanes from 150's to Gulfstreams 7 days a week. ZZZ1 is uncontrolled so I understand Tower can't control them completely but it can be prevented. I appreciate TOWERS constant and clear communication with both aircraft and I'm also thankful we all had each other in sight and the weather was crystal clear. Any sort of cloud coverage; poor visibility and not having visual contact could've been very hazardous and potentially fatal.