Dispatcher reported a ground traffic conflict during a push back with another aircraft push back controlled by ATC on a different frequency. Dispatch was contacted by ATC to resolve the traffic conflict without injury or damage.

Narrative

Operations was repositioning a company aircraft from [Gate] XX to a hardstand spot. They were halfway across the ramp when Aircraft Y entered at Spot XX for [Gate] XY. Due to where the tow was going Aircraft Y needed to turn around a go back to Ground at Spot XX. During the 180 turn back to Spot XX; Tug X with a B777 undertow started pushing off of [Gate] XZ into Spot XX without asking if we had traffic first while Aircraft Y were turning around to leave Spot XX. The FAA Tower gives the instructions for pushbacks of [Gate] XZ but all aircraft/tugs are required to call us first to verify there is no traffic at Spot XX but this did not happen; and the tug went straight to the Tower for pushback. The tug had to stop mid push to not hit Aircraft X and the FAA Tower had to call to ask what was going on. Once I told the Tower they did not verify that there was no traffic they asked how to help. I told them taking Aircraft Y off of Spot XX would be the solution. The FAA Tower took Aircraft Y and continued Tug X's pushback.