Does 2" of spray foam mean 2", or are measurements like with finished lumber?
No this is not normal.  Spray foam (or XPS/EPS foam) provides a specific R value per inch in absolute terms.  It is not at all related to how framing lumber is measured.

Rather then ask for a refund, I would ask the contractor to add more foam to meet the agreed upon thickness.  Otherwise, you are trading efficiency and long-term savings for a short-term refund.  Additionally, it would be difficult to calculate how much of a refund is appropriate. Easier to just fix the problem.