Some sea cucumbers like to just pick a spot and stay there, so it might just decide not to move. Given that you said this one started real small and kept growing, it's possible you just had all three come in at the same time, possibly from the same batch of baby sea cucumbers. If that's the case you either could have just missed them because they were so small, or the other two may have just moved over there because the conditions there are more favorable for their larger size than the previous area they were in.
Regardless, most sea cucumbers are generally safe in reef tanks (not much tries to eat them, so generally you don't need to worry about them getting overly stressed), but you should probably make sure your equipment is sea cucumber safe (i.e. you want to make sure they can't get pureed by going into one of your powerheads or something), and - as was mentioned above - they can release toxins when they die, so you'll want to keep an eye out for that. A lot of sea cucumbers will give you some sort of warning before they die (such as contracting to look short and squat - a defense mechanism/sign of extreme distress that they use to try and escape predators/death - or ejecting a cloud of toxins - because of how this actually works, the cucumber generally dies after releasing the toxins), and some of them, as long as they don't get hyper distressed, (as I understand it) won't intentionally release toxins in your tank - they just die like a normal animal, so as long as you remove the body fast enough, it won't poison your tank.
On the off chance that they do decide to release toxins into your tank, if you catch it early enough, you can run carbon, do a big water change, and (if necessary) transfer your livestock to another tank. I would strongly recommend using protective equipment in this case as some sea cucumbers when they release toxins can be dangerous to humans, but, ideally you wouldn't need to worry about it. Ideally, you'd just remove the cucumber either soon before or soon after it dies (the people I've talked to said they didn't need to run carbon or anything when theirs died in their tank, so as long as you catch it before the body starts degrading you should pretty much be fine as I understand it).
Lots of scary info there, but generally sea cucumbers are safe to keep, and as long as they are physically safe from harm in your tank the chances of them "cuke nuking" it by releasing toxins into your tank are very slim.
Hope this helps!
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