There's not a great all-purpose answer to your question, and even 99th percentile test-takers can struggle/disagree when it comes to the interpretation of modifiers. The good news is that we can usually get to the right answer without determining whether the modifier is adverbial! However, in this case we know "Once released" has to be an adverbial modifier because it is describing a condition. The album was a hit
once it was released. "Once released" doesn't make sense as an adjective: "The once released album was a hit"? "The album that was once released was a hit"? Compare it to "When I was young, I had long hair." Sure, I am the one who was young in this sentence, but only the word "young" describes me. The modifying phrase as a whole tells us when I had long hair. The same thing here: the album was released, but "once released" describes when the album became a hit. (It's not a very interesting modifier, really. You wouldn't expect the album to become a hit
before it was released, would you?
)
In any case, the vast majority of initial modifiers (modifiers that begin a sentence) are adverbial. They often seem to be adjectival, because they precede and relate to nouns, but they are usually modifying the following action:
Wanting to impress the judges, Linda added a few extra tricks to her routine.Here, it certainly seems clear that Linda is the one who wanted to impress the judges, and it would certainly be wrong to say "Wanting to impress her judges, a few tricks made Linda's routine better." However, the modifier is adverbial. It gives the context for why Linda added tricks. My rewritten version is wrong not because "Wanting . . . " has to touch "Linda," but because if we rewrite the sentence to make "a few tricks" the subject, then the verb is wrong, too. Anything that follows "Wanting . . . " will have to describe what the person who was "wanting" was trying to do.