Co-author wants to put their current funding source in the acknowledgements section because they edited the paper
In general, I would be pragmatic about this. If the contribution of the Assistant Professor is large enough to warrant co-authorship (which is a different story altogether, and not the question here), it should be large enough to mention their funding source. Presumably they have actually had to invest some amount of time into the manuscript to warrant co-authorship, and if they "used" their own university-funded research time or some external project time to contribute to the paper is really their own business.

Clearly this does not mean that you need to pretend like the entire work was funded by your co-authors grant, but a clause in the acknowledgements such as "Prof. X acknowledges the financial support provided by XYZ" is common and completely appropriate.


  I'm wondering if putting that acknowledgement would implicitly say that the co-author's current funding also funded the research in the paper.


Only if you word it poorly. 


  Maybe "Co-author was funded by Blank to edit the manuscript" is a middle ground?


This sounds very uncommon to me. I would only write it like that if you also explicitly list who paid for all other parts of the study (which would be highly unusual in my field).


  In either case is it acceptable to "use" this money to edit manuscripts from previous work done and funded elsewhere?


That's a question between your co-author and their funding source, and shouldn't really be your concern.