A320 Captain reported experiencing wake turbulence and having a communication breakdown with ATC while on final approach to the runway; in regards to whether the traffic landing on the other; parallel runway was in sight.

Narrative

Vectored approach maintain 2;000 ft. Cleared ILS Runway 22L. Maintain 180 kt. to ZALPO. On a late Tower handoff we were told we're cleared to land Runway 22L." Then; "You're following a heavy A350." At 1;700 ft. Tower asked if we saw the aircraft we're following? Dealing with trying to slow as much as possible and feeling the effects of the top of the heavy jet wake turbulence; the aircraft was blending into ground lights. I said I see a light ahead. The controller said not good enough. I said I clearly see the airport and runways. Controller said he needed to know if I saw the aircraft approaching 22 Right. I stated; "I don't see an aircraft for 22 Right BUT I DO HAVE THE AIRCRAFT AHEAD FOR 22 LEFT." Nothing further was said by ATC. TCAS showed the aircraft about 5 miles ahead and very short final. We slowed to minimum speed and continued without incident. After landing we were asked to call JFK Tower on a phone line. I spoke at length with the Supervisor and cleared up the questions together.We were "cleared for the ILS;" not for the Visual. The first time we knew we were following a heavy jet was first checking with JFK Tower. We were "cleared to land" by JFK Tower. That clearance didn't change."