How do multiple processes usually 'share' a timer?

Microcontrollers (assuming no RTOS in use), typically don't have multiple processes, they have the main thread of execution (which in the article is the entire program) and have interrupt routines that a run in response to an external event (in this case, the timer has expired).

Using the interrupt driven approach, can led to better performance both in CPU time (async communication with slower periphials etc) and battery life (sleep states).

by either having the timer fire regularly and have run code to figure out what needs to be done now, or having code to set it to the time to the next needed interrupt