April 30: Your evaluations should have been completed.
May 15: You should be notified of rating.
June 1: Deadline to submit your comments in writing.
Within 30 days of receipt of evaluation: You may initiate a review under the procedure outlined in Article 41. Section F.
Hopefully, your supervisor factored your input heavily or at least had good faith discourse with you. If your supervisor is less-attuned, perhaps your input was discounted or you received an inaccurate or unfair appraisal.
Even a glowing review could still benefit from your comments—especially when it comes to facts, figures and context. You can correct any inaccuracies, emphasize accomplishments, and add supporting attachments. You can write a narrative for each of the sections or key duties that require your commentary.
Assemble the original appraisal, your narratives and any supporting documents as one large PDF file, if possible. There is no page limit. Ask the supervisor to confirm receipt via email and that your comments will be maintained together with the appraisal when filed away.
Why does it matter?
Your appraisal could be viewed by new supervisors later. If your current supervisor got it wrong, your comments can be read on equal footing with theirs. This is yet another benefit of a union contract, and a step towards preserving your professional reputation at Rutgers.

For ‘Pro Tips’ on describing mitigating factors in your comments, see slides 21-22 of the Get SCP Ready training outline.

