How exactly is Ulfric considered a Thalmor bitch?
Well you say the Empire is the Thalmor's bitch cause we surrendered. Ulfric surrendered to the Empire, so that makes him... The Bitches bitch.
With the Thalmor stationed in his homeland and with the Imperials too weak to drive them out Ulfric took a great risk (Treason/Insurrection) to turn against his weaken empire to save his homeland from these racist creatures.
Ulfric merely completed their goal, planned since he was allowed to escape from Thalmor captivity. He was a tool, used and manipulated into tearing Skyrim asunder. If he was manipulated once, can it happen again?
Kicking Thalmor Justiciars out of Skyrim does nothing. They were funding insurgents inside Cyrodiil, hundred and fifty years ago. They don't need an open presence to do the most damage. Skyrim is weakened after the Civil War, Ulfric merely removed the Thalmor who were there in an open capacity.
They are a cloak and dagger foe, the Empire has been dealing with Thalmor infiltrations for quite sometime. Ulfric's new government lacks the shadowy ability of the Empire. There are already Thalmor sympathizes in Skyrim, Nords and Khajiit alike. You can never truly remove the Thalmor from your borders, unless you destroy them completely.
So yes, you have the Empire. Standing there, taking the bullplops and the boasting talk. Fake smiles and false courtesy, simply waiting and preparing. The Empire is heading to war. While it may seem grand to 'throw' out the Thalmor, you're merely pushing them further underground with no way to remove them.
He knows from personal experience just how dangerous they are.
So does the Empire. It is why the Empire doesn't underestimate the Thalmor, why they take this Civil War threat very seriously. Why they must put it to the sword, quickly.
They're going around slaughtering nords for doing nothing more than to worship Talos and the imperials can't do pl*** about it either. Tullus preaches about how Ulfric is guilty of murdering imperial citizens... well what the fluff has the Thalmor been doing? They've been slaughtering imperial citizens after getting the green light from the Empire regarding to the ban of Talos.
They're going around 'slaughtering' Nords to send them flocking towards Ulfric's banners. The Thalmor are playing the Stormcloaks, who are so unaware they're pawns. The Empire sees through this, and it is why they consider the Stormcloaks a threat.
You even have Tullius, saying he almost wishes to join the Stormcloaks due to the Thalmor making the Empire look bad. So both sides are angry, for Tullius, a Legion General and Military Governor to even admit he almost wants to join the Stormcloaks shows how the Empire doesn't like things either.
Tullius however doesn't act solely on emotion. So yes, the Empire merely takes the crap and sucks it up. Meanwhile they prepare and rebuild. Most of the Legions are on the Aldmeri borders, the Empire had a five year head start in preparing for the Second War. Ulfric's rebellion is helping the Thalmor catch up.
We will rule our land the way we want it.
In Aldmeri chains? Lose Cyrodiil to the Thalmor, you lose Skyrim. Pale Pass is wide open for them to stroll on through. The Stormcloaks aren't Ysgramor's 500 who had the greatest enchanted weapons and armor of their era, and also had mages.