Air Traffic Control Fully Certified
Communication Breakdown
ATC Issue All Types; Airspace Violation All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR
General None Reported / Taken
Procedure; Environment - Non Weather Related; Human Factors
A firefighting TFR recently went into effect south of ZZZ airport. Aircraft X (small aircraft) was overflying that area in a route that kept them clear of the TFR. Firefighter Aircraft Y was in the TFR and briefly flashing conflict alert with Aircraft X. Aircraft Y was in the TFR and I believe it was level at X;XXX feet when I saw it. At this point I suppressed conflict alert believing that it was conducting normal firefighting operations and maneuvering within the TFR. Aircraft X was approximately 7 miles outside of the TFR. Shortly after suppressing conflict alert; I lost sight of Aircraft Y; believing it was operating in a cluster of firefighting aircraft in the TFR; I went to perform other tasks. Less than a minute later; conflict alert went off again; I looked down and Aircraft Y and Aircraft X were separated by 100 feet and less than a mile. Both aircraft were VFR and Aircraft X was receiving flight following. Aircraft Y; a high performance jet aircraft exited the TFR; rapidly climbed and almost ran into Aircraft X that was in close proximity to the TFR. I'm unsure of weather Aircraft Y was lost on the radar at the time; its tracking on system but none of the other firefighting aircraft are. In either case; I didn't see it again until it was in close proximity to Aircraft X.  I called a traffic alert; Aircraft X acknowledged saying he had them in sight.Turbojet aircraft should be legally required to have flight following at all times.
Center Controller reported a conflict between a firefighter aircraft in a fire TFR area and a small aircraft near the TFR.