There's no "normal" way. Whatever works for you to get a structurally sound end result is right.
If you dye before fitting the binding filling any gaps with natural or dyed dust and glue can be easier.
If you fit the binding first and have to fill gaps, they won't take the dye as well as plain wood.
If you manage to get the binding air tight, either way works equally well.
For masking the natural binding the first option to pop into mind is masking tape but as you know, the dye will creep under the tape no matter what. Covering the binding with lacquer is a much better option. If you don't need it elsewhere, clear nail varnish will do instead of a gallon. You can leave the lacquer on no matter what you use for finishing the rest of the body - even if you use oil.
I guess the rubbery coating they use for masking stone prior to sand blasting might work as well. I've seen that being used for writing names on tombstones, they wipe it on and let dry, then cut and peel the letters open and finally peel the protective shield off. Then again, a gallon v.s. a tiny bottle with a brush...