Does the word “adulation” have any negative implication that the admiration or praise is more than it deserves?

If I use the word “adulation” when talking about a band like the following sentence, does it sound that the band received a bit excessive admiration that is more than they really deserved?

Or is it fine to use the word “adulation” without worrying about that?

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My favorite band, Sakanaction, basked in the adulation of the fans when they released a song called “Wasure-rarenaino.”
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In my opinion, "adulation" does carry a slight feeling of excessive admiration and praise, as you said.
But I would say it's more of a feeling that the person who is giving the praise is perhaps doing too much/going over-the-top. It doesn't imply that the person/group/band that is the object of the the praise doesn't deserve it.

So in your example, "the band was basking in the adulation of fans," it sounds quite natural. Fans often have a slightly over-the-top amount of love for their favorite bands. It doesn't imply that the band didn't deserve their praise, it's just a bit of exaggeration to show that the fans were very passionate :)