Does funding determine how many cards the Jihadist draws per turn?
Or is it determined by the number of cells on the map?
Nope, it is funding.
5.2.8 Deal. Next, deal the Jihadist and the US sides alternate cards,
up to the numbers indicated by the Funding and Troops tracks, and
begin a new Turn.
Yeah, it becomes not crystal clear in the rules (at least I do not find it).
So to make it clear, if your funding marker is in...
...the tight box: draw 7 cards
...the moderate box: draw 8 cards
...the ample box: draw 9 cards