The parties decide the evaluation between themselves, since it belongs to the applicant's own qualification. Where the employer chooses to file Form I-129 rather than send the applicant to a port, the petition and its government fee are the employer's filing.
Split the bill along the line of who owns the document
Costs in a TN matter divide more cleanly than people expect, and the dividing line is ownership of the document. A credential evaluation, a replacement transcript, a certified translation and a licence in good standing all attach to the applicant and follow the applicant to the next job. A petition attaches to the employer and to that role.
Hypothetical example: a designer near Saint-Joachim-de-Shefford agrees to reimburse the U.S. firm for half of a petition, then leaves the role after eight months and has paid for an asset she cannot take with her. Government amounts are published in the USCIS fee schedule and change, so read the current schedule rather than a figure quoted in an email last year.
Two costs get forgotten in nearly every budget. The first is time: an evaluation of a foreign degree can take weeks and cannot be compressed by paying more. The second is the second attempt.
If a refusal at a port sends the applicant home to fix a letter, someone pays for the return trip, and it is better to name that person before the first attempt than after it.