speedbar-smart-directory-expand-flag

speedbar-smart-directory-expand-flag is a variable defined in `speedbar.el'.
Its value is

t

Documentation:
Non-nil means speedbar should use smart expansion.
Smart expansion only affects when speedbar wants to display a
directory for a file in the attached frame. When smart expansion is
enabled, new directories which are children of a displayed directory
are expanded in the current framework. If nil, then the current
hierarchy would be replaced with the new directory.

You can customize this variable.