At the moment, Domestication Innovation's collar tags will work on the dragons, but the trinary command system will not. Alexthe668 offers a very useful and easy (at least from what he says - I don't code Java) guide on how to make a pet compatible with the commands system.

How?
Pls DM me the link/method.

My understanding to the system was that it was plug and play.. at least that was an advertised feature some time ago. I will look into this.

After doing some further investigation, it seems Alex (the developer of Domestication Innovation) has stated himself that the features DI offers is only included for vanilla mobs. "It is up to other mods to develop a similar system for their mobs." (his own words from the curseforge page.)

I don't foresee myself developing any sort of system like this, but I may in the future add exclusive support for DI's systems.