Definition of Rabin acceptance condition for omega automatons
As Emil explained in a comment:
The sides are interchangable when defining the Rabin condition - my professor defined the left side as the one that is required to be visited infinitely often while Wikipedia and the paper I've mentioned define the right side as the one that is required to be visited infinitely often.
Whichever the side that has to be visited infinitely often is, it can be required to be non-empty, since if it is empty, the pair is meaningless - it cannot be visited infinitely often.
It is okay not to require it to be non-empty, because if it is empty, the pair simply accepts the empty language without causing any contradiction or changing any of the desired results of the definition.