Actually, Jarl Igmund was the one who accepted Ulfric's offer to rid the city of Forsworn in exchange for Talos worship. He was not acting on behalf of the Empire but on his own accord. He was just mad that his father was killed and that he got kicked out of his hold.
True but jarl is part of the empire and the empire at the time didnt have the troops to spare so they hired ulfric and his men. And technically at the time, ulfric was also part of the empire, he didnt officially renouce until recently. And the jarl is part of the empire because of his actions, if he didnt give ulfric up the empire woulda had to go to war to soon. If he was just acting on his own behalf that in now way affects the empire, why would there be a reason for a sooner war, thats because markarth is whhere the empire gets most of its silver from making it an emperial providence hence part of the empire.
And yes im a stormcloak supporter, but as the gentlemen above their are reason to be for and against either factions and said reasons could also be countered by other side. Its all about what fits ur personality as there is no real wrong side. BUT always be aware of propaganda which unfortuantly does seem like the empire has more of to make itself look better but I chaulk it up to how the people of cryodill vs skyrim are cultarlly, whats accepting and what looks bad is different in each nation. And the bear of markarth is huge pile of lying propaganda that even the empirial jarl gives us most of the info that defutes it.