If you have a smart phone throw some tunes on that and see if it works better?
My last car was awful I had to connect my phone everytime i got in.
My current car plays where it left off on ignition.
Your car must be seeing the memory stick as a new device on startup. Hopefully there is something in the sys menu to fix that.. this ioniq came with the thickest instruction manual av ever seen.aybe try the phone and bluetooth connection, it may work as it should for you.
Its a steep learning curve.