The number of schools that invite me to talk about my books and then fail to offer my books for sale following my presentations always amazes me. This is a fund-raising opportunity lost. Plus, your students and teachers will have an autographed book as a memento of the visit. Pay the author. Most people expect to be paid after they do their work.
Authors are no exception.
If you've agreed to pay the author following the last presentation of the day, make sure the check is ready ahead of time. Have the check ready when the author arrives. If you need an invoice before you can pay, advise the author in advance so he or she can have an invoice ready. Pay the author the speaking fee before he or she leaves your school. Expenses can be paid later if necessary.