Depending on how good your microscope is, they all operate on a random clock cycle.
There are some partially async computers around. There are some truly async, clockless analog computers operating on factory floors.
Wouldn't the function yielding the random mutation have to be checked at the regular clock cycle of the computer system or some timer interval dependent upon the computer's clock cycle? Wouldn't that function have to have been programmed by somebody?
I would say this speculation is correct, but largely irrelevant. A computer simulation on an ordinary computer is going to be code-constrained by a clock. Whether this code constraint manifests itself materially in the data (the display or other consumption of the simulation) will depend on what the programmers decide to do. The random function they used is, I highly suspect, random enough for our purposes. You can find whole computer science books on this subject. We're pretty good now at for-all-practical-purposes random number generation--it's tricky, but it's not that tricky.
Isn't the "random" function, in fact, not random, but dependent upon the computer's clock cycle and the program itself? Just wondering.
Not usually. Beginners often try to generate random numbers that are, in fact, rendered non-random by the clock, in some devious manner, but by the time you are actually doing commercial work, you've figured out how not to do that.