From Jeju to Shanghai to Budapest

Hi there. I am a Hungarian citizen holding a study visa that will expire on jul.31.
I will be in Korea during this time, and will make a short stop back to Shanghai mid-August.
I already have confirmed tickets for an onward flight, so would like to make sure I am eligible for the transit.
My flights go like this:

Jeju-Shanghai (Jin Air, single trip, Aug. 15)
Shanghai-Helsinki(layover)- Budapest (FinnAir, Aug. 17)

Hope the info I provided is clear and really really hope I'm eligible...
Thanks in advance!! :)