You can think of "involved" as an adjective. Only the "are" or "were" carries the tense marker. Note the following.
We [are / were] involved in the project. We [are / were] happy about the project. We [are / were] tired of the project. We [are / were] worried about the project. We [are / were] anxious about the project. We [are / were] thankful for the project