This is what happens, and I guess this is the issue that some people don't understand (or care about, or personally have, and that's fine too). But this is what would happen to me:
(Get a message) --> Hey, Billy, I wanted to...
(Scrolls off page due to Limsa Chat)
(I scroll back to the "Hey, Billy" message, which, yes, is a scroll instead of a flick. OK, great.)
"Hey Billy, I wanted to see if you'd like to...
(Auto scroll-back)
(Scroll of the mouse wheel)
"Hey Billy, I wanted to see if you'd like to group up with me and my...
(Auto scroll-back)
(Scroll of the mouse wheel)
"Hey Billy, I wanted to see if you'd like to group up with me and my friends in about a half hour? We...
(Auto scroll-back)
(Scroll of the mouse wheel)
"Hey Billy, I wanted to see if you'd like to group up with me and my friends in about a half hour? We're going to do a bunch of FATEs and...
(Auto scroll-back)
(Scroll of the mouse wheel)
"Hey Billy, I wanted to see if you'd like to group up with me and my friends in about a half hour? We're going to do a bunch of FATEs and then probably run a dungeon. Not...
(Auto scroll-back)
(Scroll of the mouse wheel)
"Hey Billy, I wanted to see if you'd like to group up with me and my friends in about a half hour? We're going to do a bunch of FATEs and then probably run a dungeon. Not sure which one yet. Any...
(Auto scroll-back)
(Scroll of the mouse wheel)
"Hey Billy, I wanted to see if you'd like to group up with me and my friends in about a half hour? We're going to do a bunch of FATEs and then probably run a dungeon. Not sure which one yet. Any ideas?
That's how it goes sometimes. Yeah, separate chat into windows will help. Yes, a notification would help. Yes, fullscreening would help.
A toggle for "don't adjust my chat positions," would also help.
(Edit: NOTE: My personal problem with this is solved, via "methods". I only jumped in on this to back up OP when people questioned that the issue even exists.)