Learn English – Preposition in and on regarding clothes

What you call phrasal verbs have always been one of the messier parts of English syntax, and grammarians do not agree on what to call them, or how they are put together, or what to call their components.

Your first source is rather old-fashioned in one respect: it calls words like on and in ‘prepositions’ only when they take explicit objects; when they do not, it calls them ‘adverbs’. Other grammarians call on and in used in verb idioms like this ‘particles’ when they do not take objects; and still other grammarians, represented by your second source, claim that they are always ‘prepositions’, but may be used either transitively, when they take objects, or intransitively, when they don’t—just like transitive and intransitive verbs. This last version has the prestige of the highly admired Cambridge Grammar of the English Language (CGEL) behind it; but it is still contested.

Everybody, however, acknowledges that there are three different patterns, and my advice is that you focus on that. You will have to learn every single one of these idioms individually anyway, and will have to know which pattern each idiom follows. Don’t worry about what to call the pieces, just know how the pieces are used.

"...substitute for the criminal justice system..." is correct in your example. You always substitute something for something else.

I can think of a situation in which you'd use "to" after "substitute":

I used a substitute to avoid going to the grocery store.

However, in that example you're just not saying the part where you've substituted something for something else, shortening the sentence. The "to" phrase isn't telling us what was substituted; it's just telling us why something was substituted. We can include it with the other part:

I used a substitute for the buttermilk to avoid going to the grocery store.

or

I used a substitute for the buttermilk in order to avoid going to the grocery store.

The "to" has nothing to do with "substitute", which pretty much always takes "for".