ZMA Controller reported aircraft responded a RA from a non-tracked target that just appeared within altitude filter limits; resulted in a NMAC situation. Controller also reported operations manager stated this as a non-event.

Narrative

While working the radar position at Sector 24; at approximately XA:20z I received a call from Aircraft X. Aircraft X stated that he received a TCAS RA and that he was responding by turning to the left to avoid the traffic. I responded by instructing him to advise me when he could take alternate instructions. Shortly after he stated that they were probably less than 300 ft apart from the other aircraft and that I had climbed him right into the other aircraft. After he said that to me; I saw a limited mode c intruder that had just appeared and I told him that the target had just popped up on my scope and the altitude appeared to be at 8;900 ft and appeared to be behind him now. I immediately reported the RA to my supervisor and printed out the aircraft strip. When I got relieved from my position; I went to the front desk to talk to the OM about the RA. I am honestly shook up about the possibility of having a mid air collision and not being to do anything about it. The OM said it was a non event and that I handled it like a professional. However; I am not the type of controller that sees this as a non event. The fact that I climbed an aircraft right into another aircraft without even knowing that I put his life in danger doesn't sit well with me. I asked the OM to see if that target was already there before I climbed him but he said there was no way of knowing since it was below our coverage at sector XX. At the time of the incident; Sector 24 was a yellow sector with a lot of complexity and volume. We had W168; W174; and AR618 active all around the sector. On top of that; Ft. Myers Approach was instructed to close the MOOKY DTA due to W168 being active but they kept on sending aircraft right towards the warning area. I had to call them on every aircraft departing out of the MOOKY DTA and instruct them to give them a heading to avoid the warning area. It's unfortunate that this is a regular occurrence in Miami Center. If we ask for something to be closed; it'll take an hour before they actually close it; if we ask for in trail; the answer is: we'll try but don't expect it. It was about an hour after my incident that I was offered a break since we're so short staffed. During that hour; I realized how shook up I was from that RA. I started to over separate traffic from unverified mode c intruders. I'm not easily shook up by these things but for some reason or the other; this one did shake me up and I will be filing a report for this incident.Recommendation: My recommendation is as follows. We've been in a Government Shutdown since Day 0. I know that this is out of our control and there is absolutely nothing we can do about it. However; what we can do is slow down the traffic by slowing down the volume of aircraft that we work on a daily basis. Since the shutdown began; everyday we get a GI saying that there's a ground stop for DFW or in trail for JAX Center due to staffing shortages. However; there's never anything in play for Miami Center. We were already short staffed before the shut down began and now we have less people showing up to work than usual. There is absolutely no reason why we should be working yellow and red sectors during a government shutdown. All day long; all you hear in the control room is how we're not getting payed and conversation about this shutdown. What do you think this does to a controllers brain? We should be able to focus 150% on our job as controllers and the reality is that we are not able to do so due to these circumstances. People have begun to disrespect each other in the control room due to this political talk and the obvious stress of having long plug ins and short breaks to accommodate the staffing shortage. Working under this type of pressure has definitely played a negative role on myself and my coworkers. Maybe if I was able to focus more and the complexity wasn't as bad; I could've seen the mode c intruder in front of Aircraft X in order to prevent this incident. I'm sure that there havebeen a lot more incidents since this shutdown began and a lot more to come. The fact is that we need to find a way to slow down our traffic volume. Please let me know if there's anything else you need from me.Thank you