I've tried with little luck to find some origin for that expression, if it is indeed ever spoken outside my particular parlor. My only discoveries have been in late-19th century novels. Elias Power by John M. Bamford (1884) describes a "good lady" warming a teapot, adding "a pinch for each guest" and then "an extra pinch for the pot."
That squares basically with James Norwood Pratt. A seer of teaism, I asked him about this phrase. He hadn't heard it as "pinch," but said, "What I grew up hearing repeated is the hoary old 'a teaspoon per cup and one for the pot.' Both expressions are beyond tracing, no doubt, but I'll bet the pinch antedates the teaspoon."
My favorite reference though, is this passage from Frederic Morell Holmes' Faith's Father: A Story of Child-Life in London Bye-Ways (love those antediluvian titles!), because it describes the winking pleasure — the "low voice," as if doing something slightly naughty — with which I seem to have adopted this aspect of the teatime performance:
In course of time, however, he reappeared, bearing with him an old battered tin canister, out of which he ladled, with the greatest deliberation, two spoonfuls of tea, following them with a little "pinch for the pot," as he observed with a low voice. It was indeed quite a sight to see him cast in that last little pinch. He did it with such an aspect of extreme benevolence and generosity, as though he were exhibiting to the world a vastly magnanimous action, and was being cheered on by the spectators. Having done this, he closed up the canister with the usual difficulty experienced in making the lids of those articles fit on properly, and once more attempted his perilous passage across the floor.
I shall strive to restore this behavior prior to every pour.