Expected: The correct (first) project is brought to front (but behind the find window) and a tab is opened in it.
I realize the Find in Project window is associated to a project, and if you do that, then running a search on it would search the first project when then the expect behavior would be to search the second project.
So, maybe you could just clear the search results when invoking the find window from a project other than the one the results are related to.