i don't think i would have bothered tbh, but i don't think you or anyone else should be too hard on your/yourself for asking. you were uncomfortable and spoke up. it's good that he obliged you, it's part of the tattooers job to make you feel comfortable while making you the best possible tattoo. especially if it is your first tattoo interaction with them.
technically it would be sterile, especially since a fresh bottle of ink.
i get more concerned with the number of tattooers i see accessing their phones mid-tattoo (with gloves they are using on you). phones are disgusting. don't lie, everyone checks their instagram or twitter while sitting on the toilet !