If every character on the display changes when you scroll the display, it doesn't matter as Jan has said you simply change the register which tells the display which part of the data area to start from.
Its a built in command which allows you to have a line of text which is longer than the 16 characters and changing the register simply tells the display controller to display from character number 3 to number 19 for example.

so;-
Data in display memory:- 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4
display from character 0
Displayed data :- 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7
display from character 3
Displayed data :- 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1