star trek - Why were the Romulans so blase about the Dominion after it gained a foothold in the Alpha Quadrant?

At first, it was the shared belief of the Alpha Quadrant powers — Romulans included — that the Dominion could be reasoned with or, if necessary, defeated. But it became increasingly clear that both outcomes might be impossible, given the resolve of the Founders and the stunning defeat of the Romulan / Cardassian surprise attack on the Founders' home world.

This would certainly lead to a shift in Romulan policy, towards using the Dominion to defeat the enemies of Romulus instead of trying to wage a possibly hopeless war against the Dominion.

Indeed, the Romulans have always enjoyed seeing the Federation and Klingons suffer, by pitting them against each other or finding other ways to weaken them. The Romulans demonstrate this in Enterprise, Star Trek VI: The Undiscovered Country (the Romulans conspired to keep the Federation and Klingons at war), and in TNG (where they fuelled the Klingon Civil War and tensions with the Federation). Watching the Dominion dismantle the Federation and the Klingon Empire would be ultimately very satisfying to the Romulans.

Finally, in the episode "In the Pale Moonlight", Senator Vreenak explains the position of the Romulan Star Empire to Sisko:

VREENAK: You are persistent, Captain, I'll grant you that, but dogged determination isn't enough to change the reality of your situation. Time is definitely not on your side. The Dominion shipyards are working at one hundred percent capacity. Yours are still being rebuilt. The Dominion is breeding legions of Jem'Hadar soldiers every day. You're experiencing a manpower shortage. But most important, the Dominion is resolved to win the war at any cost. You and I both know the Federation has already put out peace feelers. Now, in all candor, if you were in my position, which side would you choose?

In the same episode, Dax makes a similar analysis:

DAX: Think about it. They're in the perfect position. They get to sit back and watch as their biggest rivals slug it out in a long, bloody war. No one's threatening their interests. Why should they risk their necks? There's simply no reason for them to get involved in our war. No reason at all.