Does completing this quest, which means killing Valmir, gets you a bounty with the Thalmor?

I went to Forelhost in search of Shallidor's writings for the "Shallidor's Insights" quest from the college librarian. I hadn't yet finished the College Main Questline(neither the MQ) yet so Arcano wasn't dead, so he coudn't be the reason either. Yet a little after completing "Siege on the Dragon Cult" Thalmor Justiciars attacked me and I had no idea why !

No, not in my experience. Dude will attack you first anyway.

Did you kill any Thalmor justicars in the wild or sided with Kematu in "In my Time of Need" since siding with Kematu and betraying Saadia brings Thalmor on you.

I've been attacked by Thalmor without ever doing any of those things.... I think it's just really random.

Didn't kill any Thalmor Justiciars no. The thing you say about "In my Time of Need" is interesting though, as it removes the ambiguity of the quest. Anyway I had done this quest and sided with Kematu but it was a long in-game time ago. You would think they would be faster to act on that, though it's always a possibility.