For years, employees had seen what they pay toward health

Got a PM for this.

Actually increase/increases is a non-issue here, since increase is not used as a verb in this sentence. Technically, it is called a bare infinitive (the infinitive to increase, without the word to). Since the structure of infinitives is: to + the basic form of the verb, to increases is an incorrect construct, because increase is the basic form of the verb; hence, in the bare infinitive usage also, increases would be incorrect.

From an understanding perspective, the structure of the sentence is like this:

For years, employees have seen <prices> increase.

prices would be a noun; similarly, instead of prices, what is mentioned in this sentence is: what they pay toward health care . So, the sentence is:

For years, employees have seen <what they pay toward health care> increase.

Similar to:

Jack watched his friend play.
Jack watched his friends play.
People have seen <something> increase.

As is evident, it doesn't matter whether we have singular (friend) or plural (friends), the bare infinitive remains the same: play.

p.s. I don't believe test takers need to develop concept in bare infinitives. The reason I highlighted it was to make sure that it is understood that we cannot analyze increase from a subject verb agreement perspective here, because increase is not used as a verb here.