Well for all his talk of being a shadowmaster, Tain was rather hamfisted at times. He fully announced his plans to the governments of Cardassia and Romulus(that the Federation got wind of very quick) even before he attacked. If he was successful I'd see a similar annoucement saying how badass he was for committing genocide.
Would've been way more interesting if he hadn't announced anything, just flew his fleet through the wormhole, blasted the Founders and didn't declare victory just leaving the Dominion to wonder -who- did it. Of course, I'm sure even the Dominion can technobabble CSI and find there were Romulan/Cardassian weapon signatures there.
If Tain was really clever, he'd do a false flag operation. If he's such a badass spymaster that just with the intelligence branch he can acquire the materials, facilities and knowledge to secretly manufacture a fleet of warships, it's not that much larger of a leap to acquire some Federation or Klingon ships. The Romulans nearly did this in Unification(where we see an entire junkyard or derelict Federation ships) and heck a bunch of Ferengi oafs who were beaten by kids got some Bird of Preys. If he did that not only would he eliminate the Dominion as a threat, but any retaliation would be at his other rivals.