But why all join up to side against them (the Federation)? The Feds were the ones who planted the idea of joining up in the first place. Why not join against the Tholians or the Breen?
Remember the "root beer" scene in DS9? The Federation has been the dominant political and cultural power in the quadrant for a long time, and a lot of other states see it as a bullying imperialist state, no matter how benevolent it believes itself to be. If you've been an also-ran to a more powerful entity for a long, long time, if you're sick of the way they condescend to you and try to convince you they know better than you do, then you're not likely to want to join forces with them. The Federation has a way of assimilating or at least domesticating the cultures that join it, and these groups don't want to end up drinking the root beer.
I find it very curious how a group such as the Romulan Star Empire who fought against the Dominion and suffered severe losses would so readily form an alliance with a group like the Breen who who sided with the Dominion. Storywise, it will be interesting to see a further rift growing between the IRS and RSE... but it does seem to stretch credibility a tad to suddenly be sharing currency with the Breen. I know people have pointed out that many real world nations forged alliances following wars with one another, but A Singular Destiny, pretty well the sole purpose of the Typhon Pact seems to be to serve as a thorn in the Federation's side (messing with their refugee locations, etc.). Why would the RSE join the Pact when they seem to have many more reasons to be against the Breen than against the Federation?
The RSE has a much longer history of antagonism with the Federation than it does with the Breen, so their opinion on the relative number of reasons might differ.
The idea of the Pact is not merely to be a thorn in the UFP's side, but to be an alternative to the UFP, a counterbalance and competitor. So it's attracted powers that have antagonistic motives toward the UFP (like the Tholians) or toward the Klingons (like the Kinshaya) as well as those who have nothing specific against the UFP but wish to be strong apart from it (such as the Gorn). But the disruptions caused in ASD were actions taken by the individual members
of the Pact, and halted and apologized for by the Pact as a whole. It's essential to keep in mind that the Pact, at this point, is more an idea, an aspiration, than a truly united front. There is no such thing at this stage as an action taken by the Typhon Pact -- only actions taken by the individual nations that have agreed to try to work together as the Typhon Pact. And those nations have their own agendas, their own expectations of what they want to get out of the Pact -- and who's in charge of the Pact. And yes, the members do have some bad blood between them. All that will be dealt with in the books.