Having trouble with using tables with chatted events please help?

Problem

Your only problem here is using the PlayerAdded event in a local script. You can fix this in one of two ways:

1. Server-side

You could make a server script, put it in the ServerScriptStorage, paste that code in it, and it will work fine.

2. Client-side

If you wanted to keep this in a local script, you'd just removed the PlayerAdded event and create the chatted signal on the local player, like this:

local admins = {"KingLoneCat", "Player1"}
local messages = {"Reset", "Die"}
local player = game:GetService("Players").LocalPlayer

-- Set the chat event with the local player
player.Chatted:connect(function(msg)
	for i,v in next, messages do
		for _, admin in next, admins do
			if player.Name == admin and msg == v then
				player.Character:findFirstChild("Humanoid").Health = 0
			end
		end
	end
end)

Hope this helped, let me know if you have any questions.