Why can't you just use the generator to get the hex code and copy it into a dye and use the dye on an offspring is what I really don't understand.

Basically, you do what all the rest of us do when we need a specific colour and don't know the hex: have a second tab open, open that second tab to the generator, choose your colour, go down to where it has the hex code on the bottom right (just above your saved colour boxes), copy the hex, go back to your tab that has the dye page open, paste the hex, and hit the button to use the dye.