Some might like to use adverbs. I’m not sure I’d parse those as adverbs as implying. It’s certainly a possibility, but as a native American English speaker when I think present participle derived adverbs, I tend to think of words like “interestingly”.

If both can be understood, for example, “they were crying when they left” or “he was yelling when he came” then I might instead parse it as a past progressive verb form.

Do you think

anyone has done an interview with Us Weekly?

Is verbs (present participles)? Wving, for instance, takes another straight object, his hands and the like. And that is not why we love to waving. Syntactically they are (take a deep breath before you try to say this)

• subject-oriented predicate adjectivals

That is: they play the role of adjectives in describing a noun; the noun they describe is the subject; and they occur in the predicate, among the dependents of the verb, rather than being included as attributive adjectives in the subject.

Exactly the same thing can be done with ordinary adjectives and adjectival past/passive participles, in a definite manner.

While on mission, I witnessed a boy come home wounded.
What are the effects after a youngster is brought home by something so horrible.
If you ask me what he did and I am satisfied he came home happy.
He came home naked. What do people think?

None of these describes the quality of the movement: they describe the subject.

There are object-oriented predicate adjectivals that likewise may be ordinary adjectives or present or past participles. I drink my coffee black.

It helps.
When you sip coffee steaming, he adds steam.
When I can drink coffee, this whipped cream sounds good. I just don’t have time for it.

What are some alternative ways to explain something?