General aviation Flight Instructor reported a near midair collision on the downwind leg in the traffic pattern with an aircraft also on the downwind leg. ATC separated both aircraft.

Narrative

I was the instructor during a training flight with my brother who was acting as pilot in command (PIC) of his Aircraft X; as we were in the traffic pattern; we were instructed by Tuscaloosa Tower to make left closed traffic for Runway 22; which we did; upon turning downwind; we were flying parallel with Aircraft Y who had entered the traffic pattern from the south and descended into it. Both planes were at the same spot in the traffic pattern (left downwind for Runway 22); we were flying a wider pattern than Aircraft Y.Shortly after spotting the plane; Tuscaloosa Tower instructed Aircraft Y to make a right 360 for spacing; the pilot followed his instruction and made a right turn which put the Aircraft Y pilot heading towards us during his turn; because of the relative position of the two planes; Aircraft Y turned behind us and finished the right 360.Had the Aircraft Y pilot been faster or ahead of us in the traffic pattern; evasive action would have been required to avoid a mid air collision.This event was followed by Tower instructing us to do a right 360 for spacing also; which allowed the Aircraft Y pilot to land ahead of us.I believe the cause of this near mid air collision was the Tower Controller's lack of situational awareness; I do not believe he knew we were both on the downwind until he made a mistake. There were 2 planes in the pattern and a small plane flying a practice approach inbound; as well as a jet inbound; which I believe led to task saturation for the controller and the loss of situational awareness.I also believe that the Aircraft Y pilot did not know where we were for the majority of this event; likely due to not being able to see us under him while he was descending into the pattern.