[Unsolved] Why does PlayerAdded not work properly here?

Players.PlayerAdded:Connect(function(plr)
	table.insert(PlayerIndexes,plr)
	game.ReplicatedStorage.Remotes.DisplayName:FireAllClients(FindIndex(plr),plr.Name)
end)

This Code basically adds a player who joined inside a custom leaderboard inside every player. When I start a local Server, the first player can see everybody on the leaderboard, the second can see almost everybody, with one player missing. The third player can see almost every player with 2 missing. The fourth player can see almost everybody with 3 missing The fifth player... I think you get the idea. So, Question 1: Is it only a local problem or does it happen in a real game?

Question2: If it is also a problem ingame, how do I solve it?

Thanks in advance!

You don't need a server script for this, you can just loop through all players in the LocalScript. So, you could have a script that loops through all players and displays them on the leaderboard every time a player joins or leaves.

Something like this:

local players = game:GetService('Players')
function UpdateList()
	-- clear list
	--do something with the localplayer's name and create a frame idk
	for _,plr in ipairs(players:GetPlayers()) do
		-- do something with the player's name and create a frame idk
	end
end

players.PlayerAdded:Connect(UpdateList)
players.PlayerRemoving:Connect(UpdateList)

I changed your code a little

Players.ChildAdded:Connect(function(plr)
    PlayerIndexes[#PlayerIndexes + 1] = plr
    game.ReplicatedStorage.Remotes.DisplayName:FireAllClients(FindIndex(plr),plr.Name)
end)