Government charges depend on the route: fees collected at the port of entry for a border application, or USCIS fees under Form G-1055 if the college files a petition. Reimbursement is a matter for the appointment terms.
Ask about reimbursement before the letter is drafted
Hypothetical example: a Frontenac Islands instructor's appointment letter is silent on immigration costs, and the college's human-resources office says it has never paid them. For a Canadian citizen applying at a port of entry, the government charges are the fees collected at admission for her and any TD dependants. If the college instead files Form I-129 with USCIS, the petition fee and any optional premium-processing fee apply under the current fee schedule.
She may also pay for a credential evaluation if her degree is foreign, for certified translations and for professional review of the letter. Public colleges often cannot reimburse costs that are not in the collective agreement or the appointment terms, so if reimbursement matters it must be negotiated into the offer before she accepts, not claimed afterward. Renewals every three years, and a new application if she moves to a different institution, carry the same charges.
Hypothetical example: A Frontenac Islands geology instructor receives a reimbursement promise stated only in an email from a department chair. A first review should separate mandatory government charges from optional translation, evaluation, and professional-review expenses, then ask the college which ones its policy permits it to reimburse. The collective agreement or written appointment terms settle that question.
Paying before the approval decision does not guarantee repayment later.