For paid abilities, it’s not quite that simple. First the cost resolves, then all the cost’s cascading triggers, then the ability, then the ability’s cascading triggers. There’s an example in the UFAQ on Quarantine System. So if this is like a paid ability that costs a click, then it’s Seidr first. Incidentally, things can be triggered in the middle of an ability, too, as when Leela steals an agenda while accessing multiple cards from HQ.
But as you said, this isn’t a paid ability, so it could very well be quite different.