Great question! Let's look at it this way. A sentence, no matter how long or complicated, has only two parts: a subject and its modifiers and a predicate and its modifiers. A subject is the person/s we are speaking to or about or the thing/s we are speaking about. A predicate is whatever we say or write to or about the subject. Think of a predicate as a box of information. It might have lots of other information in it, but it must have a verb. A subordinate clause like "when I see closed doors" is, as you say, like an adverb, which modifies the main clause "I get the willies." As a modifier of the predicate, it is also part of it, just as a simple adverb would be. Hope this helps!
