A319 Captain reported that the ECAM HYD Y RSVR LO LVL appeared while in cruise. As the flight crew ran and followed the QRH and checklists; there was confusion regarding a procedure with a hydraulic pump. After consulting with Dispatch and Maintenance Control; the flight crew performed an air turnback.

Narrative

At approximately FL350 in cruise; the ECAM HYD Y RSVR LO LVL appeared. ECAM actions were followed and after completion; the ECAM HYD Y ENG 2 PUMP LO PR appeared due to turning off the Eng 2 Pump as directed by the first ECAM. After completing the ECAM; Dispatch was contacted and Maintenance Control was patched in. After consultation with Dispatch and Maintenance Control and discussion amongst fellow crew members; the decision was made to return to ZZZ. [Priority handling was requested]. While in the turn the flight attendants were called and given a briefing. Shortly after; a PA was made to the passengers briefly explaining the situation and that we would be returning to ZZZ. As the ride was smooth; the FAs (Flight Attendant) were permitted to finish the service that they had already started in order to give a sense of normalcy and calmness in the cabin. Once the 180-[turn] was completed; ATC provided a route direct to ZZZ where we advised that we would require Runway XXR for landing due to its length. After making the turn back to ZZZ; we realized that the aircraft would be overweight upon landing so a descent to FL240 was requested from and granted by ATC. This was due to attempting to burn as much fuel as possible to be as close as possible to maximum landing weight upon arrival. The Overweight Landing Checklist was completed while still in cruise back to ZZZ. Landing distance was calculated by both Dispatch and myself and the values came to within approximately 200 ft. of each other at around 8;500 ft. This gross error check satisfied us that the calculations were accurate.While in cruise back to ZZZ; discussions were had regarding status page notes and stopping technique. It was noticed during discussion of status page notes that the ECAM had the crew turn on the electric yellow hydraulic pump during the approach phase while neither of the non-normal checklists in the FM (Flight Manual) contained that procedure. As the accumulator pressure was dropping slowly and the concern of losing any remaining fluid existed; the decision was made to follow the status notes in the FM non-normals section and not turn on the yellow electric pump during approach. A normal approach briefing then took place. Once the aircraft neared ZZZ; ATC provided vectors overhead for a right downwind to [Runway] XXR. The aircraft was configured early due to flap movement being slow and the desire to have extra altitude in the event another malfunction occurred. We were then vectored for approximately a 15-mile final where a visual approach was conducted. The autopilot was selected off at approximately the FAF to get a feel of how the aircraft would handle while having the yellow hydraulic system inoperative. A normal landing was made and the aircraft exited at Taxiway XX. After exiting the runway the aircraft was stopped and emergency vehicles surveyed the aircraft. Ground personnel advised that there was no evidence of hydraulic fluid on the aircraft. Emergency vehicles then cleared and the aircraft was taxied to the ramp where the engines were shut down and a tow-in was made to the final parking spot.Prior to the tow-in; the yellow electric pump was turned on momentarily to charge the accumulator in order to set the parking brake prior to shutting down engines and completing as much of a normal procedure as possible. After turning on the yellow electric pump; the hydraulic SD page was referenced and we noticed that the fluid quantity had dropped slightly. This led me to believe that if the pump was turned on according to the ECAM status notes during the approach phase and not left off according to the FM non-normal status notes; that all remaining fluid would have been lost. After shutting down the engines and waiting for the Tow Team to connect to the aircraft; it was discovered that the Tow Team did not have a headset available to communicate to the cockpit with. Instead; the busy Ramp frequency was used to communicate with the Tow Team; which led to confusion and a slight delay in getting the aircraft to the gate. After completion of the parking checklist; appropriate maintenance write-ups were made and debriefings took place with the crew; Operations Control Flight Operations Representative; and Chief Pilot.