(Important note: d20 is the system used by D&D, if that helps explain things)
Well, a Stand should have hard-written effects. However, for the purposes of combat encounters, it becomes necessary to codify when they can apply those effects in a dice-based scenario. In other words, people have hard-written abilities as their in-character "superpowers," rather than as a function of their game role. So, the antagonist no longer has "kill" as an automatic game ability, but rather must accomplish killing using their defined abilities within a statted scenario.
Let's take a Stand from the series as an example:
Crazy Diamond is a Stand that can repair anything it touches, including living things. However, it cannot heal its user, and it cannot revive someone from the dead, even if it restores their corpse to pristine condition. These are all hard-written abilities, and follow only those written limitations outside of a combat scenario.
However, within combat, where timing is important, we need to clarify several things within the rolling system. For example, how long does it take for Crazy Diamond to reach out and touch something? How long does the repair process take? For the purpose of the test game, we decided that the repair ability would cost a bonus action, and could be applied to any one thing aside from the user within its own tile or an adjacent tile.
As far as the relevance of the wider background of Jojo's Bizarre Adventure, well, Jojo consists of a series of only tangentially connected stories. This game need not involve any characters, locations, or events in common with those of the series. Therefore, the important thing for all players to understand are the rules about the setting's powers.
Please do help point out unexplained jargon, though. You know how it is: once you're in deep enough, it's hard to see it. I tried to give a basic definition of Stands and their rules in the OP, but I don't know how well it explains it.