Once the just-described timer interrupt portion of the scheduling housekeeping work is done (and, of course, these things are done very quickly indeed), control is handed back to the process context (the thread, current) that was rudely interrupted. It will now be running what we think of as the exit path from the interrupt. Here, it checks whether the TIF_NEED_RESCHED bit is set – the need_resched() helper routine performs this task. If it returns True, this indicates the immediate need for a reschedule to occur: the kernel calls schedule()! Here, it's fine to do so, as we are now running in process context. (Always keep in mind: all this code we're talking about here is being run by current, the process context in question.)
Of course, now the key question becomes where exactly is the code that will recognize whether the TIF_NEED_RESCHED...