When can we change the order of the particle and the verb in a phrasal verb?

As noted in the comments, phrasal verb is a slippery term that has been variously defined. Indeed, the Cambridge Grammar of the English Language states (p274): We do not use the term 'phrasal verb' in this grammar.

However, if we follow the definition given in the foreword of the Collins Cobuild Dictionary of Phrasal Verbs, then phrasal verbs are "combinations of verbs with adverbial or prepositional particles".

So the answer to your question: "When is a phrasal verb not followed by a preposition?" is "When it is followed by an adverb(ial)." For example: to steal away, to cut back.

Other phrasal verbs have particles which can in other contexts function either as an adverb or as a preposition: to put down, to get across, to come about.

The last group contains particles that can only function elsewhere as prepositions: to make do with, to get at, to make of.

The question in your title is a complex one. The textbook that you refer to should be able to help you answer it.

For me, phrasal verbs have to do with grammaticization and therefore are never followed by a preposition. However, the part that gets added to an otherwise self-respecting verb sure looks like preposition, but it's not. If you have a phrasal verb, that erstwhile preposition is now part of the verb, and we can call it a particle. What makes this whole thing a thing is the fact that the meaning of the verb plus particle is different that if it were just verb and preposition.

Grammaticization is like lexicalization; both processes create new units of meaning. Over the course of time as we use constructions like jump at to mean something similar to seize that 'at' feels more a part of the verb than the noun that it was associated with, you can think of it as deriving a new verb. And with grammaticization, as in this case, the deriving of the new verb happens over time and through use. You can also think of this new verb as being transitive, which it must be, if you agree we have a particle attached to a verb.