Yes. Act is one of those verbs. But it can work both ways. "He acts tough" is similar to "he is tough." It means, he acts (behaves) in a way that makes him appear TO BE tough. The implied TO BE calls for an adjective rather than an adverb. So the correct sentence is "he acts tough," not "he acts toughly." You can also use the verb "to act" in a way that does not imply "to be." For example, an actress can act badly. That means her acting is bad. She herself is not bad. Here, the emphasis is more literally on her "acting," not her "being."

“He acts tough” is the short form of “he acts as if he were tough” . When you frame it like this it becomes quite clear that tough is not and adverb that describes the verb (to act), but rather an adjective to describe the noun (He). An adverb is an optional device that describes how someone is doing something (the verb). In the case of acting.... the verb itself is vague, but it defines a hypothetical action that can benefit from specifics as in that phrase above. Specifically with act, word order would come into play.... since it requires an adjective after the verb to describe the noun, if you were to use an adjective also, it would need to come before the verb. “He cautiously acts (as if he were) tough.”

-ly generally indicates an adverb and reflects back to the verb, to act. When you say someone acts tough, you are meaning that they are tough, or they’re giving the impression that they are. If you were to say he acts toughly (which is also grammatically correct) it means something slightly different—it reflects on his acting, and not him.

act + adjective = the adjective is the object of the acting, i.e. what the actor pretends to be he acts dumb, he acts tough, he acts confident (usually followed by 'but...') act + adverb = the adverb describes the acting itself, e.g. he acts well, he acts beautifully. in theory you could use both, e.g. he acts dumb well, i.e. he is good at pretending to be dumb. It gets confusing when 'act' has the meaning 'behave', e g. he acts with integrity, he acts like a clown. But if we stick with 'act' in the sense of 'pretend', the above description should be adequate!

But I think sometimes the implication of saying it that why is act as in put on a show, like an actor. For example, "he just smokes cigarettes to act all tough". Implying that he smokes cigarettes to act like he is a tough guy