Hi
The answer to your questions lies in the bold text following RF7 in the Scott catalog (at least in the 2010 revision that I have).
To paraphrase, some of the manufacturer's overprints are cancellations AND surcharges (i.e. they change the value of the stamp), while after RF16 the manufacturers' overprints simply became cancellations.
So, yes, the "8 Cts." in red was applied first, by the Bureau of Engraving and Printing, and then the cancellation(s), of which there are many, was applied by the manufacturers.
Even trickier than your example is this one:

This appears to be the rare RF15, but look within the inverted "c 8" cancel and you'll see the "8 Cts." surcharge, which makes this stamp simply a RF16. This stamp is very frequently seen at dealers and auction houses, being represented as a RF15.
A "real" RF7a looks like this:

Hope this helps.
Jim