To answer you question: It doesn't matter if the adjective comes before or after the noun it's describing, but the user might do that just to simply add emphasis. "Li estas aliulo, ne mia koramiko." is also grammatically correct, but it may lose the emphasis that the user might have wanted to portray.
The reason for this is that Esperanto's rules make it flexible for native speakers of different languages to change the way they speak and still make sense. For example, "Mi mangxas la rugxan pomon" (Germanic syntax) = "Mi mangxas la pomon rugxan" (Romance syntax) = "Mangxas mi la pomon rugxa" (Celtic syntax), etc. In these examples, you can see that the noun-adjective relation is changes, as well as the positions of the subject and object. For the noun-adjective relation, a noun and its adjective(s) can be in pretty much any order as long as they both have the same ending (-n or not) and are in the same part of the sentence(e.g. they must stay on the same side of "kaj" and "ne" in large sentences, or else it won't make sense). The other part is the subject-object relation. In this, the subject and object can move around the verb, as we know which one is which because of the -n ending, unlike other languages where the placement defines if it is a subject or object. Hope this has helped, and not been confusing.
For anyone in general who wants to learn more about grammar in more detail, go to en.lernu.com and go under the learning tab at the top. Lernu is also a great resource for Esperanto overall, with forums, a dictionary that can not only translate between many languages but also deconstruct an Esperanto word to its roots and affixes, and even its own Esperanto learning program.
Thanks for the answer. I was aware of the flexibility of the structure, but wondered whether there are slight preferation when expressing a certain meaning. The thing is, linguistically, it would be very interesting to investigate that with Esperanto mother speakers, because the flexibility is first and foremost a certain simplification for learners. For mother speakers that feature would be too loose, it has to be divided into more meaning, like putting emphasis on the adjective/possessive pronoun lets it be after the noun. It would be interesting how mother speakers are attributing meaning nuances to the syntax of the adjective or other words.
When I was learning about the accusative, Someone put it that this makes it so that you arrange the sentence in whatever way you need to change the emphasis, and that it helps separate which adjective belongs to which noun without having rules about where in relation to the noun the adjective is. As far as how often this allowance is utilized, I am not sure, but it is something to be prepared for.