I think it’s necessary to sort out the complements, the compliments and the supplements.
Complimentary means flattering or paying compliments that are remarks of admiration or respect. You pay someone a compliment.
The adjective is also used to indicate given for free as when someone can get you complimentary tickets for a show or concert, often given for the sake of publicity
A complement can be a complete entity as used in the phrase a full complement ie all the officers and crew of a ship. It can also be used as the thing or person completing the whole.
Complementary suggests adding on to what is already there as in complementary medicine like for example acupuncture together with diet and other factors keeping you in good health.
Supplement is an addition of some sort often used to describe an extra magazine sold with a newspaper. It could also be something added to your food to improve an aspect of its effectiveness
Supplementary also suggests added on /in addition to. In parliamentary debates for example members often ask one question and then add a supplementary question related to the first and added to it. In this sense it’s not necessarily needed to make something complete as with ‘complementary’
So we come to your quote:
This means, I suggest that it (whatever ‘it’ is) should be looked on as both completing the submission ie making it a whole and also adding something extra to it.
My compliments to you.