Ramp Tower Observer reported a ramp incursion when ramp push back personnel did not follow Ramp Tower instructions and a ground conflict occurred with another aircraft. The ramp personnel realized the lack of spacing between aircraft; stopped; and pulled the aircraft back into the gate.

Narrative

Aircraft X; Gate X called for push and was approved. They were unable to push because vehicles were being stopped behind them. Aircraft Y; Gate Y called for push shortly after and was initially told to hold. Gate X was unable to push because Gate Y failed to ask permission for doing an engine start at the gate; meaning the vehicles were stuck behind Gate X until Gate Y pushed back. Instructions were amended and Gate X was told to hold; Gate Y was told to push tail north. Once Gate Y was unhooked; the vehicles cleared and Aircraft X; Gate X informed me their ramp said they were ready to go. I gave them the conditional; once the 737 behind you taxis; push approve tail north." The read back was correct. They almost instantly started rolling back on the push and I immediately informed Aircraft X to stop the push; which they acknowledged. Aircraft X was unable to get in contact with the ramp and continued pushing back. I believe the ramp eventually realized there was not adequate spacing and stopped the push; with the wingtips of both planes appearing to be within a few feet of each other. Aircraft X was pulled back into the gate until Aircraft Y; Gate Y taxied out."