This paper by Fausk, Hu and May does not exactly tell you why those maps should be isomorphisms in more concrete situations, but it cleanly explains the abstract settings in which they arise - look e.g. at Propositions 2.4 and 2.8 for equivalent formulations of projection formulas.
For an example of a projection formula that is not on the list in your question see equation 2.2.5 in this book by May and Sigurdsson - it is an example for the abstract "Wirthmüller context" from the paper above, which, I think, inspired the authors to do the abstract analysis in the first place.
