Well, they are out of the pot and soaked, so whether or not you did things wrong or not does not really matter any more.
However, it is the middle of winter and even if where you are the winter may be reasonably mild, soaking plants that are generally not happy campers to be really wet when it is cool/cold and there is little light, the timing of your efforts is probably a little off. You now really want to make sure they dry out quite well and then repot them and not water them for a good long while.
The fact that the roots where coming out of the bottom of the pot, definitely signaled they needed to size up a pot, but timing... aside from time of year, I'd also not repot right after watering it made you encounter the issue that had you then wash the plants. It does not necessarily hurt to remove all the soil from the plants you are repotting, but it does increase the chance for major damage to the roots which can be a source of problems when the plants are back in soil and you water to soon or the new soil is too wet. Unless you have serious cause to change all of the soil out when repotting (say because it is really poor soil for the cactus, part of the plant had developed root rot, or some similar issue) I tend to not be too worried if most of the soil stays put and I just back fill the new pot as necessary.
What is done is done, just be careful watering cacti in winter when it is cold and possibly humid.
One last comment. Your plants look healthy, yes the PP has some spots developing, but they do that especially when things are gloomy and not warm, but nothing in your plants appearance would suggest the idea that they have major root rot problems going on. So the suggestion to wash the soil of to inspect the roots for rot seems a little out of nowhere.
Anyway let those plants dry out really well and then carefully repot them and hold of watering for a good number of weeks.
Good luck!