Now that you asked....I'm cofused...This rule doesn't apply to all adverbs, but to "já", which seems to behave a little different from the others.
In statements, when it means "already", it comes immediately before the verb.
Eu já cheguei (I've arleady arrived). / Nós já estamos em junho (We are already in june). / Ele já ganhou a luta (he has already won the fight).
When it's imperative, meaning "now", it comes after: Venha já! (Come now).
In other cases, there's more freedom.
Já vou / Vou já (I'll go in a little).
"Já estou indo (another already case, I'm already coming)" is different from "Estou indo já (I'm going soon / I'm going in a little / I'm going now)".