If a single source does damage to multiple targets at once, Justice will add up all the damage done and deal damage to the source’s controller at one time (not multiple separate damagings).

The damage done by Justice is done as a triggered ability, which is added to the stack just after the red creature or spell deals its damage.

Justice : règles, fonctionnement et interactions (MTG)

Justice is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

At the beginning of your upkeep, sacrifice this enchantment unless you pay . Whenever a red creature or spell deals damage, this enchantment deals that much damage to that creature's or spell's controller.

How it works : Justice

Original English text — Wizards of the Coast / Scryfall

#1October 4, 2004· Wizards of the Coast
If a single source does damage to multiple targets at once, Justice will add up all the damage done and deal damage to the source’s controller at one time (not multiple separate damagings).
No other card is named in this ruling.
#2October 4, 2004· Wizards of the Coast
The damage done by Justice is done as a triggered ability, which is added to the stack just after the red creature or spell deals its damage.
No other card is named in this ruling.

Interactions with other cards

These cards' text mentions Justice.

Mob Justice

Mob Justice deals damage to target player or planeswalker equal to the number of creatures you control.

Murdock's Crusade

Teamwork 4 (As an additional cost to cast this spell, you may tap any number of creatures you control with total power 4 or more.) Choose one. If this spell was cast using teamwork, choose both instead. • Street Justice — Exile target creature with toughness 4 or greater. • Legal Justice — Exile target enchantment with mana value 4 or greater.

Justice, Vance Astrovik

Flying When Justice enters, return up to one target nonland, nontoken permanent to its owner's hand. Whenever another nonland permanent you control is returned to its owner's hand, put a +1/+1 counter on Justice.

Arrows of Justice

Arrows of Justice deals 4 damage to target attacking or blocking creature.

Evincar's Justice

Buyback {3} (You may pay an additional {3} as you cast this spell. If you do, put this card into your hand as it resolves.) Evincar's Justice deals 2 damage to each creature and each player.