Vader is relatively vulnerable while in the bacta tank, so it makes sense to protect him with the Royal Guard. If Vader was ever attacked while in the bacta tank, the guards could defend him until Vader got back into his armor.
Although we do not see the Royal Guards protecting Vader in his meditation chamber on Vader's flagship Executor, Vader's castle on Mustafar is much more secluded (and therefore less protected) than Vader's flagship. There are plenty of stormtroopers on Executor to protect Vader whenever he is meditating on his flagship.
Vader's castle on Mustafar is where Vader lives, so Vader would likely need to receive transmissions from Palpatine regarding Sith business. That means the guards there would know of Palpatine's secret (that he, too, is a Sith Lord), and only the Royal Guard is trusted to know that secret:
[Vader] seldom saw his Master so publicly demonstrate his power. And he understood what it meant, of course. There must be no survivors who could bear witness. Only the Royal Guards could be allowed to live—only they could be trusted never to reveal what they’d seen, or even to talk about it among themselves.
Lords of the Sith, p. 168
Hence only the Royal Guard could be trusted to protect Vader at his home. Stormtroopers, security droids, etc. could not be sufficiently trusted.
As far as I know, this is the only instance in which the Royal Guards are seen guarding someone other than the Emperor. Even so, the Guards are largely ceremonial since the Emperor can protect himself.
