The code works for me; might be a problem on your side but try increasing the wait time (try 0.5 seconds) because if I had to guess the tween was just barely not done and it changed the size right before it had finished.
Just did some changes for you to improve with performance.
script.Parent.Parent:GetPropertyChangedSignal("Visible"):Connect(function()
if script.Parent.Parent.Visible == true then
script.Parent:TweenSize(UDim2.new(1,0,1,0), "InOut", "Sine", 13)
task.wait(13)
script.Parent.Size = OriginalSize
script.Parent.Visible = true
end
end