Seems like there should be a procedure they would follow for the first x days.
There most certainly is, about 30 days at least, and it should have started already. You're in the same limbo many new pool owners find themselves: trying to maintain a warranty and dealing with a builder that doesn't know much about pool water chemistry and its effects on new plaster. It's actually ridiculously common for builders to not understand pool water at all.
They'll come tomorrow, dump in whatever they're going to dump in, and it'll be up to you after that. Let 'em do their thing, then begin the "real" startup process the minute they leave. If push comes to shove, they'll have to prove you did something contrary, and they're not going to be in your yard monitoring you. If they indicate they'll be back in a few days or weeks, then we'll deal with that.
Review the startup processes Allen gave you (
here), pick one, purchase whatever materials necessary for the one you select, including a proper test kit (one of the two we recommend,
here) and a good pool brush, and go to it. You can start buying things today, order the kit for sure (or restock the one you have). Keep a log of everything you do.
Take notes about any conversation you have with the builder. Write him a follow up email tomorrow after his startup, that summarizes what he did and said. It doesn't have to be antagonistic. Just short and sweet: "Thanks for the visit today. Just wanted to jot down some notes and share them with you to make sure I have them right. You performed your startup process today, and used xxx and yyy in the pool. You instructed me to do the following: blah, blah. You mention that I should: blah, and that you would blah, blah." Like that. Don't make it sound like you're going after him (you're not), just that you want to make sure you're both on the same page. Including that you'll be taking over the rest of the start up procedure after he leaves. Hopefully he'll respond, and unless he says "No, we'll be handing that," or whatever, then you'll be good-to-go to take over the startup, and he can't later give you any warranty bs.
On a somewhat obscure positive note, the fact that your pool is green and getting greener, while not great, does indicate that there's something wrong with your water, which you're going to address soon, and so it's very likely to get bluer, perhaps as blue as you want, and this'll all be behind you in short order. It's too soon to worry about the color, so, you know, don't yet.