Flight Instructor reported a NMAC at a tower controlled airport.

Narrative

On Date about XA:45 local time; I was working on traffic patterns with a student at ZZZ. We were in the left downwind of the traffic pattern on Runway XX. Abeam the end of the runway we were instructed to fly a right 360 degree turn; upon the completion of the turn we extended the downwind; then were told to complete another right 360 degrees turn. While exiting the second turn; we were given a traffic alert at 11 o'clock. I spotted the traffic in the right traffic pattern for the same runway; along with traffic on final. It was under my assumption that I was then able to turn final after the aircraft. I began to turn towards Runway XX; then I received a traffic alert in my aircraft; so I took control from the student; lifted the wing and saw the Citation crossing over the top of my aircraft. I turned out of their path towards the left; and rejoined the downwind. The Citation went missed; due to the resolution advisory they received. I extended the downwind; and was cleared to land. I was not instructed to contact the Tower; but did so myself in hopes to resolve an issue if one arose. I believe this could have been avoided by asking us to extend the downwind for traffic farther out. After leaving two 360 degree turns within a short distance of one another makes it hard to pick out traffic; in which was supposed to be referenced.