Though you say its evenly divided we never actually see many stormcloak supporters in Winterhold or Dawnstar, hell Ulfric doesn't even care about winterhold as for Riften the whole Rift is controlled by Maven Black-briar and has more imperial influence then stormcloak. Now you can make the same arguement with the silver-blood but the silver-blood don't care who actually controls the reach, only that they can do their little scam by using the forsworn as angry and sometimes disobedient puppets to drive away competitors and to take over land and mines.
The war was in a stalemate before Tullius arrived, and as I said, Rikke herself mentions Ulfric's growing support. Of course not everyone is a sold-out partisan. Most people just want to get on with their lives. If you're saying only a couple people here and there support Ulfric, however, that just doesn't make any sense. The whole quest line is built on the premise that only the dragonborn's influence decides the conflict. If Ulfric's support is so weak, then the legion must be really pathetic.
But still my point still stands that theres no proof that the Empire is actually a puppet of the Thalmor and if you actually paid attention you'd know that they dragging their feet when it comes to the WGC, as someone said before.
I wouldn't call them a puppet, rather a rump state for the Thalmor. Tullius grumbles about having to bend over for the Thalmor but that's still what he does. It's not his fault, he's a good soldier and just following orders. They aren't really dragging their feet too hard, though. All of them show up at Elenwen's parties and Tullius is not above using the Thalmor to take out undesirables (as in the Missing in Action quest, where he could ask for Thorald's release if he wanted to).