That is correct.

It's not always a preposition. For example, a quick check of the definition for "up" tells us that it can be a preposition, an adverb, an adjective and even a noun or verb (transitive and intransitive). Whew. "In" has the same thing, except no verb examples. The same applies to other short words, and that's even before we get to phrasal verbs. Hopefully, you're providing phrasal verbs in context. Point out how the meaning can change if the different elements of the sentence change. It really depends on the greater context. Also, if you take the (what shall I call it?) "non-verbal" part of the phrasal verb away, then you can show how the meaning changes again. I'm reluctant to classify any phrasal verbs as idiomatic. It just seems like a cop-out.

Some have certain rules, for example prepositions of place (in at on, for example) and prepositions of time (in at on, for example) Some take the form of phrasal verbs. For example Get up, get on ...