The Markarth Incident is useful because it gave them the ability to operate in Skyrim more directly, but theres no indication anywhere in game that they instigated it. The Thalmor are not the only group antagonistic to the Empire in Tamriel, and a big part of their MO is taking advantage of other, unrelated threats to advance their agenda in an area. Its how they came to power, after all.
Of note, the Markarth Incident is where he forms his army and starts acting on his own agenda more directly, as well as surrounding himself with other advisors and the like rather than acting as a lone individual.