org-agenda-move-date-from-past-immediately-to-today

org-agenda-move-date-from-past-immediately-to-today is a variable defined in `org-agenda.el'.
Its value is

t

Documentation:
Non-nil means jump to today when moving a past date forward in time.
When using S-right in the agenda to move a a date forward, and the date
stamp currently points to the past, the first key press will move it
to today. WHen nil, just move one day forward even if the date stays
in the past.

You can customize this variable.

This variable was introduced, or its default value was changed, in version 24.1 of Emacs.