Will it mess my engine up by switching the gas I put in it?
It depends if your car recommends Premium (92 or 93 octane) or not to be honest. Some cars have internal sensors to help with compression ratios. Having a later model Tiburon I'm sure running unleaded is the safest although higher octane levels will cause more of a combustion gaining the slightest bit of power. Research whether or not the engine can handle higher octane levels before you do it. Apologies for a vague answer. After all, premium is only what an extra $3-$5 a tank?
Search Hyundai Tiburon Questions
Are you a UK consumer? CarGurus now has a discussion forum in the UK.
Hyundai Tiburon Experts