What process is described as the behavior of voters when they assess incumbents (and vote accordingly) based upon their performance in office?

There are two types of choices when one makes a vote:

The Rational Choice: A "rational" voter is conscious that voting is a personal right that is attributed to each and every one of the citizens of a given country. It is up to that voter's criteria to discern which candidate to vote for. The Collective Voting Choice: A "collective" voter will probably tend to conform with a group he or she belongs and vote according to the choice that the group has convened to be the best. People that belong to political parties or other organizations tend to be collective voters.

Regarding the case mentioned in the question, when a voter assesses a candidate's past performance, regardless of the political affiliation of this candidate, he is engaging in a "rational" vote.