So how did Ulfric get captured by the Jarl and get handed over to the Thalmors?

Because the empire needed a scapegoat. Just one man against the town guards when he isn't expecting it isn't really that difficult.

Edit: Also I'm not sure what relevance this has to the eyewitness accounts of what happened during the incident. Ulfric's arrest was some time afterwards.

So that proves that him and his men were there all the time, not the mention that Silverblood is a faction friendly to Ulfric. It could have easily been Ulfric and the Silverblood family influencing the Jarl as your source suggests.

Keep in mind that Ulfric in 4E 175-176 was not the same Ulfric we see now. He was a relatively young man, was only a Jarl's son and not a Jarl (much less one that was contending to be High King), and did not have the kind of clout or importance that he does when the game opens 25 years later. He's a young war veteran and former POW who comes home to find that there is a small local war going on in Skyrim that the Empire is unable or unwilling to address, and he forms or agrees to lead a local militia created to deal with it on behalf of one of Skyrim's other "royal" families.

To argue that what happened at Markarth was somehow part of a grand 25-year-plan to one day kill the High King and secede from the Empire is also a bit much, lol. Not that you are saying that, but I've seen others talk about the incident in precisely that fashion.

Doesn't make sense. Ulfric was captured by the Thalmor during the Great War. The assault on Markarth was after the Great War.

Yes, Ulfric did kill the Forsworn but how else are you going to take over a city? And the Forsworn are hardly a good ruling army, if they can't hold Markarth a near impregnable fortress.

Good, I am not the only one that sees that and does not overlook it.

But just out of curiosity, why do they want to avoid a Stormcloak victory since technically it weakens the Empire?

They'd have a war on two fronts. As it is now. They can monitor all of the legion's movements due to the WGC and plan their forces accordingly as a precautionary measure should the empire suddenly back out of the treaty. They'll be prepared for it. In a nation that absolutely despises the thalmor and works against their agents, gathering intel is much more difficult. Agents are killed, captured, interrogated, etc. It's difficult to know the full strength of their enemy or what they're doing. If the forces of skyrim attack soon, it means the dominion can't keep all their forces on the cyrodiil border, which the imperials might take advantage of.

Basically it creates an unknown in the Thalmor plans. And when you run your army through tactics based on intel as the thalmor do, having unknowns is very dangerous.

Ahhh I see now. Thanks for clearing that up!

Basically the Thalmor want the Empire to be strained to the limit, resources depleted, weakened by internal strife, without them losing the freedom they have to wander around Skyrim doing what they've been doing. If Ulfric wins, they lose that freedom. If he wins quickly, you could argue that their hopes were dashed on both accounts.

And let's not forget that there's more to it than just having access to the territory for intel gathering and planning. Preventing and stamping out Talos worship is, for the Thalmor, a worthy goal in and of itself, as well as a means to an even greater end (in their opinion). It's not like they are using the necessity of enforcing the ban as an excuse to be in Skyrim just to do other things.

Ulfric is uncooperative with the Thalmor.
Tullius is very cooperative.

Doesn't mean he likes that he has to be.