That’s exactly what happened the last time I bought a car. The salesperson didn’t seem to understand the concept of not negotiating monthly payments. Then the sleazy finance guy tried to get me to sign an agreement where they changed the numbers.
Don’t be afraid to get up and walk. Last year I nearly bought an Audi A6, but when they started to play with the numbers at the F&I office, I got up and walked.
They had already detailed the Audi and moved my license plate and personal belongings over. I made them put everything back.