There is no PID loop in the sense you mean. It's a hardware counter module that feeds a flip flop. There might be a free running ADC that is used to compare match against the counter module, or sometimes it's just a binary input like the AC signal zero crossing.

You don't need a CPU core to do this, and the older, cheaper parts do not necessarily have a CPU in them. There are even (iirc, very uncommon) designs with no digital logic save the switching.