Between the first offer and the actual contract, the salary quietly drops. Each round of negotiation shaves a little more, usually justified by a claim that you are 'not fully qualified'.
Write the agreed figures into an email summary after every call and ask them to confirm it. A number that moves before you sign will move again after.
Poster declined the offer. The school then said declining could affect future work visa approvals — a pressure tactic, not a rule.