Adulting represents behavior. That's fair enough. When you behave in a manner consistent with an adult, that would be considered adulting. Adulting also means doing the things that make you a successful adult.
Adulting in texting is pretty much the same thing, with a slight nuance to it. If someone were to text me, “Hey, what's up?” while I was adulting, I would text back, “Oh nothing, just adulting as usual.” There's a sarcastic undertone to it.
Adulting originated in a tweet all the way back in 2008. That tweet read: Grew up in a town of 2k and adulted 10 years NYC. Same values: Keeping the job. Feeding the family. Educating the kids. Buying the stuff. — unholytwerp
If you make your bed every morning, you will have accomplished the first task of the day. It will give you a small sense of pride and it will encourage you to do another task and another and another.