"justo" means right/fair/just. It also translates to "immediately following," as in this example?
Justo después de as a phrase translates to "immediately following" or "right after". The justo is an adverb that serves the same purpose as "just" does sometimes in English.
Why is "del" used here? There is no of the, by the, or from the in the translated sentence or implied (to my knowledge).