Yo,
She's trying to keep the upper hand, by turning your tests "Text me tomorrow" is a shit test if it's coming from a woman, so you should handle that in the way she did.
The way she goes "No, you text me..." is what a PUA would do.
Way's of countering this depend on your personality, but I think you did ok.
I did that once with a woman, She told me her name, again, we'd met a few months before, and I said I'd try to remember it on one condition, and pointed to my cheek in a vague way (I was shitfaced drunk

I still don't remember her name)
She said she wouldn't kiss my cheek, and I said "don't be so forward, I meant a hug", to which she blushed and complied. (not really a smooth way of handling it, but I halfassed an upper hand there

)
If she says no, call her on being shallow for not giving you an apology.
If she then admits to thinking you meant a kiss you bust her balls for that.
As to how to treat her, treat her as though she's already your lover, relaxed kino, not making a big deal out of touching her.
Upcoming shit tests, yes.
She'll be wanting to take charge, but you stay Alpha, don't comply to her wishes without getting something in return.
E.g. She wants a drink, give her the money and tell her to go buy drinks for both of you, and be a little specific about how you want the drink to give her a challenge, like 3 cubes of ice and stuff like that, if you order whisky be specific about brand and age and how it is to be served (you get it).

(credit to Kezia)
any shit-test you turn around, to being a test of her. (as mystery says, She wants you to jump hoops, take away her hoop and get her to jump it herself)
Don't give her a straight yes, ever.
David D goes through that
Get you a drink? No, you get me a drink.
call you? no, you call me.
Come over here and kiss me? No, I'm doing something right now, I'll come over later, or, You come here and give me a kiss.
Hope it helps some

(But I must admit to being only rAFC not quite PUA...yet

)
cheers, and good luck