If, for example, you're talking about a series of texts in which you respond to someone's first text, even though new texts have come in, and then you respond to the next text, even as the other person responds to your first text, well ... I don't think there is a name for it because it's so ubiquitous that it's normal. Example:
Alex: Hey, are you coming over to watch the game tonight?
Alex: By the way John says he can't make it, he's got the kids.
Alex: Oh and grab a six-pack on your way? I'm low.
Brad: I'll be there, but probably late. Who else is coming?
Alex: OK, that's fine, kickoff is at 6pm
Brad: Sorry about John, but family ya? What kind of beer?
Alex: Sam and Rick said they'd come by.
Brad: Oh man Rick?
Brad: Dude is gonna talk the whole game.
Alex: Whatever kind of beer you want.
Alex: Yeah about Rick but Sam is bringing him so what ya gonna do?
Brad: K see you later on.
I'd call this a disjointed conversation, in which the questions and responses are out of whack but nevertheless comprehensible.
Skewed is also possible, or jumbled, or discontinuous, in which questions and answers are flying all over the place.
A technical person might call it an asynchronous conversation (as FumbleFingers suggested) which is accurate, but I don't think that would be meaningful to the average person.
However I would not call it confused or incoherent (or many of the other synonyms of disjointed) because the participants mostly understand each other even though the responses don't match up with the previous texts.
(Edit) More formally we could define this as a lag between query and response, which you could call a delay of some number of conversational cycles. Anyone familiar with these terms (and how they relate to asynchronous communication) would easily understand what you mean.