Tidus has eyes, so he can see the guy leave. Whether he does that with the transgate himself or not, Tidus is no newcomer to transport machines, so following after with that doesn't more than a moment for him to appear with the blue colouration into the stores.

And out he comes, into the lower kitchen with its rows of sinks. And if this God of Death is actually in here for cleaning, then that's where he'd be.

"So, why's a guy who does stuff with death big into helping out with the sleepover? You close with Della?"