A319 Captain reported the tail of a B737 aircraft went over their wingtip during pushback.

Narrative

Prior to pushback the tug driver said he was ready for brake release. We knew we did not see the NWS (Nose Wheel Steering) DISCONNECT message on the upper ecam display and I told him that. He said 'Oh yeah;sorry.' We got that fixed and he pushed us back fairly quickly and left us 6 feet right of the lead in line. There was a 737 to our right and we did not have much clearance with it. The tug driver then asked to disconnect headset but the NWS DISCONNECT message was still there and I told him to fix it. He said something like 'oh yeah' and we got that fixed and I cleared him to disconnect. Then the 737 to our right was aware how close we were as we exchanged glances with the captain. My FO stated that his wingtip is clear as he turned out to the right. Both the FO and I watched him turn and instead of doing a 120 degree turn he did a 180 degree turn and the FO and I perceived that his tail went over our wingtip; at gate XX. We did not feel comfortable with his 180 degree turn.