No, you don't need to tell the lab how you exposed something, just how they should develop it (normal, push one, pull one, etc.) How you expose it up to you.
The main thing is that it helps to put a grey scale at the head of the roll, exposed for what you consider neutral, so overexposed if you are rating the stock slower than normal. Then put a note to time for the grey scale. The people processing the roll can't see it (until it is processed) but the print timer or telecine colorist after that will.
This way when the overexposed chart comes up, the timer or colorist knows to make it look normal in brightness so that the scene that follows will also be brought down to normal.
Otherwise, how is a timer to know, if the first thing that comes up on the roll is a dramatic scene, that the bright look was intentional or not?
I go even further - besides the grey scale, if the scene that follows has a deliberate color cast, I shoot a sign that says that, like: NOTE TO COLORIST: WARM GOLDEN LIGHT or ORANGE SUNSET or FIRELIGHT or DEEP BLUE MOONLIGHT or KEEP GREEN CAST FROM UNCORRECTED FLUORESCENTS etc.
