1. Hell no, don't pay a dime.
2. Get the survey and find out exactly where the property line is. Didn't you have one when you bought the house? Check your paperwork. Also check with the county to see if they have one. You have to resolve this question ASAP. Otherwise, that neighbor is going to assume the property line is where they want it to be, and start jacking with it more without your permission.
3. After you get the survey, call the company that did it and ask WTF? Do they often do work like this? Tell them you're going to nform the BBB, Yelp, Google Business, etc. if necessary. If you have to pay for the survey, get the company to compensate you at least that much to avoid a lawsuit.