How to make an event happen on only the Client that clicked the button/part?

I've been trying to make a Click for Cash button in Roblox, only to find out that the cooldown/debounce can also happen to other players. I've tried switching the Scripts to Local Scripts, but it does not work (I'm a beginner at coding) This is my code right now (Getting Money Script):

local cooldown = false
local COOLDOWN_TIME = 10

local Players = game:GetService("Players")
local plr = Players.LocalPlayer

local clickDetector = script.Parent.ClickDetector

local timeRemaining = 10

clickDetector.MouseClick:Connect(function(player)
	if cooldown == false then
		cooldown = true
		player.leaderstats.Money.Value = player.leaderstats.Money.Value + math.random(1,200) * math.random(1,500) - math.random(1,5000)
		repeat
			print(timeRemaining)
			wait(1)
			timeRemaining = timeRemaining - 1
		until timeRemaining == 0
		if timeRemaining == 0 then
			cooldown = false
			timeRemaining = 10
		else
			return
		end
	elseif cooldown == true then
		return
	end
end)

(Cooldown Appearance Script):

local cooldown = false
local CD = script.Parent.ClickDetector

CD.MouseClick:Connect(function()
	if cooldown == false then
		cooldown = true
		for count = 10, 0, -1 do
			script.Parent.Parent.ClickGiveMoneyBase.BillboardGui.TextLabel.Text = count
			wait(1)
		end
		script.Parent.Parent.ClickGiveMoneyBase.BillboardGui.TextLabel.Text = "Click this Button to Give you CASH!"
		cooldown = false
	elseif cooldown == true then
		return
	end
end)

More clearance to my problem: When a player clicks and cooldown happens, it not only happens on the player that clicked the part, but also on other players in the server.