Assuming that you didn't request the applications to start at start-up in the past (definitely possible to do), I wonder if you are only closing the window and when you restart have left the option to re-open currently open applications (which appears in Restart confirmation box) selected.
Multi-window apps such as Word or Pages do not close until you use command-Q or menu->Quit. The red dot only closes the window, not the application if the application can do multi-window.
Also, if you didn't know, command+tab brings up visual of all currently running programs. You can select them to quickly go between applications or quit them before shutdown in case that is to blame also.