How did "When" become the customary answer to "say when"?

I can't answer how, but I can say when.

According to the OED:

say when, colloq. formula used by a person pouring out drink for another, to ask him to say when he shall stop; also ellipt., as a reply to this formula.

The question is at least from 1889 and the answer from at least 1911:

• 1889 John S. Farmer Slang and its analogues past and present: ‘Say when,’ said Bonko, taking up a flagon of whiskey and commencing to pour out the spirit into my glass.
• 1911 Maclean's Mag.: ‘Say when?’ I held the glass with a shaking hand: ‘When.’
• 1931 A. Powell Afternoon Men: ‘Say when, sir,’ said the waiter. ‘When,’ said Pringle.
• 1948 E. Waugh Loved One: ‘When,’ he added aside to the young man, who helped him to whisky. ‘Right up with soda, please.’

I found an earlier example of both question and answer in Rudyard Kipling's A Conference of the Powers (1890):

Following the first great law of the Army, which says ‘all property is common except money, and you’ve only got to ask the next man for that,’ The Infant offered tobacco and drink. It was the least he could do; but not the most lavish praise in the world held half as much appreciation and reverence as The Infant’s simple ‘Say when, sir,’ above the long glass.

Cleever said ‘when,’ and more thereto, for he was a golden talker, and he sat in the midst of hero-worship devoid of all taint of self-interest.

I'd been looking for something like this. My girlfriend and roommate (both born in Mexico and had lived a significant portion of their lives there) just did not believe me when I said Americans reply "when" when someone says "say when." For reference, my roommate says he'd just say "that's enough" or "thank you" while my girlfriend says "like that" (a phrase which usually throws me off, and I end up putting a bit too much of whatever we are using on whatever we're eating).