Lifesteal System not working.

I tried to make a lifesteal system and after me and my friend tried to test it everything went wrong.
{
    "display": {
      "icon": {
        "id": "minecraft:player_head"
      },
      "title": "Untitled",
      "description": "Killed Player Trigger",
      "background": "minecraft:block/oak_log",
      "frame": "task",
      "show_toast": false,
      "announce_to_chat": false,
      "hidden": true
    },
    "criteria": {
      "req": {
        "trigger": "minecraft:player_killed_entity",
        "conditions": {
          "entity": [
            {
              "condition": "minecraft:entity_properties",
              "entity": "this",
              "predicate": {
                "type": "minecraft:player"
              }
            },
            {
              "condition": "minecraft:entity_scores",
              "entity": "this",
              "scores": {
                "graceTime": 0
              }
            }
          ]
        }
      }
    },
    "requirements": [
      [
        "req"
      ]
    ],
    "rewards": {
      "function": "gssmp:killed_player"
    }
  }

When we were testing it, when I killed him it triggered for both of us.
And the player got killed advancement didnt trigger at ALL.
{
    "display": {
      "icon": {
        "id": "minecraft:player_head"
      },
      "title": "Untitled",
      "description": "Getting Killed Trigger",
      "background": "minecraft:block/oak_log",
      "frame": "task",
      "show_toast": false,
      "announce_to_chat": false,
      "hidden": true
    },
    "criteria": {
      "req": {
        "trigger": "minecraft:entity_killed_player",
        "conditions": {
          "entity": {
            "type": "minecraft:player"
          }
        }
      }
    },
    "requirements": [
      [
        "req"
      ]
    ],
    "rewards": {
      "function": "gssmp:killed_player"
    }
  }