I don't think there's any cause for alarm. The dark spots at soil level in the first picture of the new set may or may not be something to be concerned about, depending on whether they get larger and/or become soft. So keep an eye on them, otherwise the rest looks within normal limits given the history. If someone else here disagrees, I hope they speak up.
Where are you located? Given these plants were in the ground, I'm assuming somewhere that winter cold is not a problem. Are they back in fast-draining soil? Were they in the sun before you got them? Assuming you're in the northern hemisphere and not in the tropics, it should be pretty hard to provide too much sun this time of year. Wait a week after potting them up, or putting them back in the ground, to water deeply for the first time. From there on out water deeply when the soil is dry at depth. And make sure they are potted up at the same level they were to start with, ie. with the same parts buried that were buried before and the same parts above ground that were above ground before.
It's generally a bad idea to dig up cacti when you're concerned about their health, unless you are looking for something specific associated with the roots. Every time you do that you damage the plant. Which may not be a big deal, especially if you wait to water, but why cause potential harm when you're already concerned about the health of your cacti. It's especially important to avoid doing this repeatedly. Others may disagree, this is just my own opinion based on personal experience. What's done is done, this advice just for future reference.
Newly installed plants often go through some changes, presumably related to transplant shock, in the weeks to months afterwards. I think that's probably what you've observed. Best to leave them alone, watch the water, and continue observing closely. I can try to give more specific advice about watering based on the location and whether you have chosen to keep these plants in pots or the ground.