never used hyundai tran fluid before
flushed mine myself 3 times using my shops bg flush machine with no problems
I use our basic trans fluid with bg conditioner
my shop uses the same trans fluid and if required we use a bg conditioner which works as an additive
since i've been an employee at the shop for six months now(been doing my sidework at the shop for a couple of years) i've never seen a car come back for trans problems because of a flush with the wrong fluids
i've seen cars that had never had the transmission serviced before(high mileage cases) that have blown seals from rot but never had one return from using our trans fluid
I have 83,000 miles on mine with zero transmission problems and have done 40 or so flushes myself to other makes and models including hyundais with zero returns.
If the shop is a franchise take it up with the franchises district manager if applicable they have insurance and will take it up with insurance. If they admit it was their fault then you will have a good chance. If they don't take blame for it you might have a tough time. There are other routes but they will take forever. If the car had never had the transmission flushed before and had above 75,000 miles on it your case won't have a good chance. Most places recommend the service every 30,000 miles, I do and some cars I recommend every 20,000 like most toyotas. They might cry negilgence.
anyway good luck