Are you sure, they are Jem'Hadar? Among the Tsunkatse spectators, there are lots of re-used species from DS9, that should not be in the Delta Quadrant. Memory Alpha lists no Jem'Hadar, but Kressari, who look a little bit like Jem*Hadar. Maybe you mean them?
Well, there are other races like the Jem'Hadar (in appearance). In The Undiscovered Country Kirk fights with another prisoner that bears a remote resemblance to a Jem'Hadar (even though it is clearly another, and presumably Alpha/Beta Quadrant species). The race we see in Tsunkatse could be a race in appearance much closer to the Jem'Hadar, much like there seemingly are races (almost) indistinguishable from humans, despite not being human. For all we know, the Founders just took the racial template of an naturally existing race, modified it with traits desirable to them (loyalty, short life, desire to fight, etc) without modifying their appearance, but left the original race untouched.
I guess the latter would work a lot better. Were the former to be true, I'd think we would have heard of these difficulties at some point (say, when our heroes capture alive a bunch of Jem'Hadar in "One Little Ship"). ...Which need not be "we will face difficulty getting white in the future and want to dodge that". Getting free of the addiction would be a victory in its own right, an achievement that will not only help these particular Jem'Hadar in practice but will also spite the Founders. Timo Saloniemi
It's possible the Founders have deployed a lot of ships long range to explore the universe to seek out threats.
Apparently, they don't even need ships to travel, as shown in Chimera they can turn themselves into one.