The way I understand it is that your colon will work harder to reclaim water if you’re dehydrated, so staying hydrated will help keep stool softer overall. That said, rehydrating while constipated (or immediately before a bowel movement) won’t make a real difference since the water has already been absorbed from the stool and it can’t add it back.

I would imagine your drinking lots of water before, if you do it consistently, is probably just contributing to your overall hydration which makes it easier next time.