What you need to know is that Master's Ultimate when active gives him attack speed, movement speed and slow immunity. The rest are not relevant for what it actually does. Fizz Ultimate slows the target's movement speed thus even when you tag him with it, he is immune to the slow effect but he should take the full damage. Other than that he will not debuff himself from the entirety of the ability and normally this will not happen.
Other than that, I notice many times where master Yi is getting Hit while in alpha strike where he is considered non-existant in the game because he is not even in the minimap. There is something off with the on-hit chain of rageblade+Doublestrike interaction. Kinda he applies on hit effects with double strike 2 times like rageblade but doublestrike is considered to be 1 auto attack that hits twice. Generally many things about master Yi's micros are out of place or logic.
Besides all that, Qss normally removes all CC effects, that is all.
Old Qss could remove all debuffs which means everything that is considered as negative buff, like any tag the enemy does to you or any status the enemy added to you, like Zed's death mark, Riot replaced it in order to give room to how much you can actually counter with it but overall it is very strong still. Merc Simitar removes all CC effects, gives a burst of movement speed that decays and for the next seconds you are less effected by CC effects, which means the CC effects will stay on you for less time.
Something is definatelly missing though, if the shark comes out when yi stands on top of the marked area he should take the damage, and finally my understanding about what could have happened would be that Fizz's Ultimate is actually a tagged slow.
Which means Master's Slow Immunity did not allow it to stick to him, think of it as a sticky-slowing-timebomb. Anything that counts as slow cannot affect Master when his ultimate is active.
Hope that helped.