I was wondering, is a monster's hit dice tied to its size 100% of the time or are there exceptions?

There are always exceptions. If you mean, in terms of the published stuff, I cannot immediately think of one off the top of my head, but there have been exceptions since the 1st Edition.

I have a certain sea creature (a whale) that can convert the water it takes in as ballast into Hydrogen and oxygen, and then expel the oxygen. It can, then, float up, out of the water (becoming a "flying whale). It should have both a lot of hit dice and they should be big.

It has a d8, and 10 of them. They are whales, and so they have all sorts of good stuff folks like, and the whalers go after them. If I made them too tough, then whalers couldn't get to them. Given I already made them tough strategically (they are "smarter" whales, who know perfectly well what whalers do, and they are vengeful, angry whales, so they fly up and then drop down on whaling ships), doing so would make them too great a challenge.

I have a group of small, compact, dense monsters who have a d12 and have 20 of them. I cannot reveal more because they are a problem that is faced down the road. Wait, I can note that their AC is 12.

One of the things you can do fairly easily is to switch up a hit die or a the number of them to move a commonly encountered being into a higher "level" of opponent -- to use a pokemon phrase, you can evolve your monsters.

In *any case*, however, one thing to keep in mind is that changing those things can change the CR of the monster.

But can they be changed, and are their examples in the published monsters? The answer to both is yes.

As far as I am aware there are no exceptions in this edition.

So, in terms of rules, I did a quick glance at the DMG: https://www.dndbeyond.com/sources/dmg/dungeon-masters-workshop#CreatingaMonster

Therein, the hit dice of a monster are indeed only limited to creature size.

Nor does flipping rapidly and doing spot checks of my Motm, MM, or Volo's indicate any exceptions.

Nevertheless, as a DM, you are completely able to do so. ANd, as is obvious, I have, lol.

But I have also changed the Sizes (there are more, and they use a 3' basis) and the possible die types (because I use additional dice), so it appears I was too used to doing things my way.

I apologize.