This sodium/potassium balance is not trival nor is it easily explained or controlled.
I take both a diuretic and an ACE receptor blocker. I do lose potassium and supplement it periodically. I find it easy to tell when my potassium level is low, my resting pulse rate increases too high.
Interestingly my normal pulse my entire life was 80. As I got older, it dropped and my blood pressure went up commensurately. After I started on diretics, my pulse rate gradually increased, presumably as I lost excess?? potassium, not sure but it is my thought. Now as it tends to get near 90, I take some potassium and down it comes.
BTW potassaium chloride is what is commonly referred to as salt substitute, it is also what is used to stop the heart in lethal injections if memory serves.
You're correct about that method of execution.
As your diuretic makes you increase the volume of urine produced, the total volume of blood is contracting and blood pressure drops. To maintain adequate perfusion and oxygenation the body compensates by increasing the heart rate.