ZMA Center Controller reported a spillout resulting in a NMAC with an air carrier.

Narrative

Aircraft X was cleared into and operating within the CAPE A ATCAA (ATC Assigned Airspace); within a block altitude of surface to FL300. He is supposed to remain within the confines of the airspace at all times. Aircraft Y was a TPA arrival to the north of the CAPE A ATCAA; and had a crossing restriction of ZINGR at 17;000. I transferred communication of Aircraft Y to F11 (Orlando Approach) in a timely fashion; and continued working. While attending to other aircraft at the sector; Aircraft X keyed up and stated 'We are finished in the area and would like to cancel services'; or something to that effect. As my eyes scanned back to where he should be; I immediately noticed that the aircraft was well outside of his assigned airspace; and was now descending directly towards Aircraft Y; who was now descending out of 17;000 feet and into MCO approaches airspace. I instructed Aircraft X to amend altitude to 17;000 due to traffic; and advised him that he was well outside of the CAPE A ATCAA and to fly heading 180 to try and get him back into the appropriate airspace as quickly as possible. Within the next target 'hit' or two; Aircraft X's altitude continued to descend thru 17;000; and I told him to stop his descent immediately and advised that there was traffic directly underneath him at 16;000. The targets merged with approximately 200 feet between them. This all happened within the span of 15-20 seconds; with me advising the D-side position to call MCO approach and apprise them of the situation. Aircraft X should never have left his assigned airspace; and did not comply with any altitude clearance given to try and prevent a collision; leading to an extremely unsafe situationThere never would have been an event if Aircraft X had remained within his assigned airspace as cleared. It's nearly impossible to predict when and where a 'spill out' like that can occur; given the nature of their maneuvers; speed and altitude changes are while they operate within said airspace. If he had remained inside the assigned ATCAA there would be no incident