no- you just copy and paste the colour hexes (eg, D47BFF, FFFFFF, 78F0F6) from generator to regenerator, or use the colour quicksave bar.
So you have your colour design in the generator- you then can save the colours there (the 10 most recent saved/used colours make up the colour quicksave bar), you get the regenerator v1 open for the pet in a different tab. You can then select each of the colour slots on the regenerator and select the intended colour from the quickload colours
(I usually do it in two groups- EC-C3 (4 colours), then the genes/must/accents (8 colours))

Umm..That is confusing..especially for someone who doesn't do this much.
Sounds like a lot of trouble having to do the ol' copy-pasta thing but that's what we are stuck with I guess.

What happens if I made changes in the generator, have the tab open then hit 'Confirm Regen in the V2 regenerator?

Let me rephrase this..let's say I have made the changes I want to my Nykterie in the generator (I have the generator and the regenerator open in their own separate tabs)..now the instructions in the Re-Generator tells me to go there (the regenerator) to confirm the changes.
If I hit the big green button to confirm my choices how can I be sure the changes I made in the generator will register in the Re-generator as there is no preview option.

I don't want to go through all that trouble to get my pet the way I want only to lose it all.

In short and in clear instructions, how do I save those changes and make sure that they will transfer to the regenerator?

Whatever you do in the generator will not end up on your pet unless you change it on the regenerator page. The generator is just a recommendation to make it easier to see what you're doing as you play around with the colours/traits.

So what I did, was copy the image url of said pet into generator, play around until I got what I want, then save the colours in the generator.

Then I go to said pet, click regenerate, the colours that I saved in the generator will be shown in the regenerator. So I change the colours in the regenerator, then click confirm.

Yes..I finally got that part. lol
However my other problem was that I didn't realize I was stuck with traits I didn't want so all I could really do was monkey around with the colors of the traits that pet already had.

Can't swap out any traits so..I think I got it.

Thank you though. :)