I think the key is that potassium levels can fluctuate drastically if the conditions are right, which is dangerous, if the person is susceptible to that. So you want to rule that out, even if it means taking too much and then backing off.
But importantly, some are prone to low potassium and some are not, and last I checked, we didn't know why. I looked back at records from childhood and saw that even then, I had very low potassium (although it raised no red flags at the time). My sense is that it's probably genetic and/or a long term abnormality, like an autoimmune disorder that you can be predisposed to. Others have other possible explanations.
Fredd has a description of the approximate hours for food potassium to be utilized, along with supplemental potassium, and how long they last, etc. I think some of it depends on your system, but generally he is pretty accurate. Although it should only take 20 minutes for something like potassium gluconate to have an effect, for me, it really takes about 40 minutes, and then depending on how depleted I am, the relief typically lasts about 2 hours or so. If I take it regularly throughout the day, I have less rollercoaster effects where I need it badly and then it barely lasts 2 hrs. Also, I take it as a powder that dissolves in water to avoid gastric issues.
It's great if you don't have to take it. One of the problems with potassium deficiency is that a lot of other things can also cause the same symptoms, so it can get confusing as to how much to take and when. Over time, it gets more clear.