Why Does This Client Sided Rotation Script Rotate On The Server?

Hello, I made a pet and I would like for one part of the pet to rotate on the client, so that the rotation doesn't lag.

However, for some reason, it seems that it makes the whole pet model rotate, on the server only. On the client, it works perfectly. This is the server sided pet follow script

local pet = workspace:WaitForChild("FlyingEmojiTemplate")
local runService = game:GetService("RunService")
local remoteEvent = game.ReplicatedStorage:WaitForChild("turnFan")


function givePet(player)
    wait(5)

    if player then
        local character = player.Character
        if character then

            local humRootPart = character.HumanoidRootPart
            local newPet = pet:Clone()
            newPet.Name = "FlyingEmoji"
            newPet.Parent = game.Workspace

            local head = newPet.HeadEmoji
            local heliCopter = newPet.HeliCopter
            local sunGlasses = newPet.SunGlasses

            head.Anchored = false

            head:SetNetworkOwner(player)
            heliCopter:SetNetworkOwner(player)
            sunGlasses:SetNetworkOwner(player)
            newPet.Parent = character

            remoteEvent:FireAllClients(heliCopter)

            local bodyPos = Instance.new("BodyPosition", head)
            bodyPos.MaxForce = Vector3.new(math.huge, math.huge, math.huge)

            local bodyGyro = Instance.new("BodyGyro", head)
            bodyGyro.MaxTorque = Vector3.new(math.huge, math.huge, math.huge)


            local rv = bodyGyro.CFrame.rightVector

            runService.Stepped:Connect(function()
                bodyPos.Position = humRootPart.Position + Vector3.new(1, 1, 2)
                bodyGyro.CFrame = humRootPart.CFrame * CFrame.Angles(0, math.rad(90), 0)

            end)

        end
    end


end

game.Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function(char)
        givePet(player)
    end)
end)

This is a localscript inside replicated First

local runService = game:GetService("RunService")
local remoteEvent = game.ReplicatedStorage:WaitForChild("turnFan")

remoteEvent.OnClientEvent:Connect(function(part)
    runService.Stepped:Connect(function()
        part.Orientation = part.Orientation + Vector3.new(0, 5, 0)
    end)

end)

The rotating Part is welded to the pet model.