You can use:
in reply to Auto-scrolling scrollbars with Perl Tk
From the docs:
Adjusts the view in the window so that the character given by index is completely visible. If index is already visible then the command does nothing. If index is a short distance out of view, the command adjusts the view just enough to make index visible at the edge of the window. If index is far out of view, then the command centers index in the window.
UPDATE: you can also see:
$text->yview(moveto => fraction)
$text->yview(scroll => number, what)