Here is how it works :

It is week 1,

Chef Sanchez is in the restaurant, Sanchez is Mexican and he is going to cook Mexican food,

Day 1 : quesadilla. Day 2 : burrito. Day 3 : enchilada. ...... Day 7 : pozole.

Week 1 is over, now it's week 2

Chef Sanchez goes away, chef Silvio comes, Silvio is Italian,

Day 1 : spaghetti. Day 2 : ravioli. Day 3 : pizza. ..... Day 7 : lasagna.

Week 2 is over, Silvio goes away, a new chef comes

And so on

Now, about the app,

When it's week 1, Sanchez is here

People vote, they can only vote Mexican foods ( what Sanchez can cook )

When it's week 2, Silvio is here

People vote, they can only vote Italian food,

This is how it works, and everything makes sense