And if it's a Trent, the starter rotates the N3 spool.
There is logic in the autostart that checks for rotation of the other spools when the high rotor reaches some limit- if rotation of the other rotor(s) is not detected by that point (it's a function of the engine type) it's assumed the rotor is locked and the start is aborted.
BTW, while autostart is basic on the 777, it can be turned off (flight deck switch) and manual start procedures used. On the later Boeing widebodies (787, 747-8) we got rid of the switch - it's autostart all the time.