When a potato cooks, the starches contained in each cell are released as the cell walls break down. These starches absorb the potato’s internal moisture and swell and soften. These two processes are what transform a raw, hard potato into a cooked, softer potato fit for mashing.
If you cut your potatoes up before boiling them, the starches absorb the internal potato moisture as well as the water in which they’re being boiled. If they boil for too long, they absorb too much water and your mashed potatoes will become gummy. The difference between perfectly cooked potato pieces and soggy pieces can sometimes be as little as a minute or two.
An easy workaround is to boil potatoes whole. They’ll take a bit longer to cook but you can leave them in the hot water after boiling without undesirable effects, keeping them warm until it’s time to mash them. I start my potatoes boiling as soon as I begin cooking and mash them immediately before dinner.
If they need more moisture, you can add a bit of hot potato boiling water or another liquid. This way, you have more control of their moisture content.
This is your problem. It isn’t that the potatoes absorbed too much water while cooking them, you left them to continue cooking in the hot water which is why they are getting overdone. You are trying to compensate with larger mass to make up for letting them soak after cooking, which is why they absorb too much water.
If you just pulled them out and made them when they were done they wouldn’t turn into soggy messes and you would have a lot more control over when they are done. If they are done early, they will retain their heat just fine in a covered dish.
The fact that you can overcook them in a couple of minutes when the total cook time cut is around 10-15 minutes depending on size is right in line with cooking pretty much anything. Cooking pasta for a couple minutes longer will change their consistency too!