SR-22 pilot reported a NMAC with another aircraft that was resolved with ATC intervention.

Narrative

I was a pilot of the SR22 (Aircraft X). I identified Aircraft Y from ADS-B data after the flight.Aircraft X was cruising beneath the ZZZ Class B outer shelf at 2;500 feet MSL on an approximate 345 heading. Aircraft Y was to its left and converging at the same altitude on an approximate 120 heading. Source: ADS-B data. Both were talking to ZZZ [TRACON]. Aircraft X was VFR and received traffic advisories. Aircraft Y was talking to ZZZ [TRACON] at the time.Aircraft X pilot could see Aircraft Y on onboard traffic display; but did not receive a traffic alert. During a hand-off to the next controller frequency; a different voice came on the radio - perhaps a supervisor - excitedly instructing Aircraft X to turn left immediately and descend. Coincidentally; Aircraft Y had received instruction to alter course to a 090 heading. This turned Aircraft Y left and across the flight path of Aircraft X. Controller instructions to both aircraft had their pilots turn left; whereas right-of-way rules required the pilot of Aircraft Y to give right-of-way to Aircraft X; and both pilots to alter course to the right.