How do I change the skybox for only a specific client after touching a part to trigger it?

any idea why my local script is changing everybody's skybox instead of only the player who touches the part? this is a LocalScript in StarterCharacterScripts

local skybox = game:GetService("Lighting").Sky

game.Workspace.SkyboxTriggers.LotL.Touched:Connect(function(hit)
    if hit.Parent:FindFirstChild("Humanoid") then
        local player = game.Players:GetPlayerFromCharacter(hit.Parent)
        if player ~= nil then
        skybox.SkyboxUp = "rbxassetid://6115435142"
        skybox.SkyboxDn = "rbxassetid://6115431284"
        skybox.SkyboxBk = "rbxassetid://6115432902"
        skybox.SkyboxFt = "rbxassetid://6115433855"
        skybox.SkyboxLf = "rbxassetid://6115430469"
        skybox.SkyboxRt = "rbxassetid://6115432137"
        end    
    end
end)

When the player touches the Part called "LotL" the skybox changes as intended, but for every player. The server does not see this change.