Hello S,
It is not a matter of waiting until you hear any noise or experience a breakdown. The valve adjustment is to keep the engine running efficiently and avoiding major damage due to a push rod jumping and getting pinned at the edge of the rocker saddle which bends them.
I usually recommend a valve adjustment check every 250 hours as preventative maintenance. (Kohler recommends every 500 hours, but that is stretching it.)
Parts wear inside of a running engine regardless of whatever kind of oil is being used, so don't prolong your oil changes.
There are some very good professional small engine people on You Tube who can show you the procedure. Avoid the ignorant DIY "goobers" who talk to the camera the entire time. Donny Boy small engine and Teryl Fixes All are pretty good. Teryl likes to make ignorant skits and wear fake teeth & hair, but he knows his stuff with all kinds of small engine equipment.
EDIT:
In this fast-paced (busy) world people tend to always be in a hurry to jump on a mower, then wind up the engine and drive like a NASCAR driver to get the grass cut. When they are done, they rush to shut down the mower engine and move on to the next task on their schedule.
As for the engine still trying to run for a second after cutting the key off, I suggest you make sure the engine is at a low idle for about 30 seconds to slow down the engine momentum, then turn the key off. If you shut down at high RPM, the engine is very hot and will try to keep running due to high cylinder temperatures that will still combust the fuel being drawn in, even with the ignition turned off.
Some diehard purists would say it needs an "after run solenoid". Those solenoids are nice when (and if) they work, but they get sticky due to the fuel. Practically all fuel ages quickly and has refined additives in it that gum up, or people use a "snake oil" fuel stabilizer (pick your favorite flavor).
I have found (from many years of small engine experience) that installing a simple shutoff valve in the fuel supply line is much more reliable. All a person has to do is idle the engine down, then shut off the fuel valve to let the engine wind down to shut off.
The important thing is to remember to cut the key off to prevent the battery from draining down.
By using a fuel shut off valve, it also helps remind people to slow down for a second and check their oil level before turning the fuel on and firing the machine up to put it to work. Lots of small engines have been ruined due to low oil volume.
