The moment you've earned at least 200 reputation from anything (excluding the association bonus) then that day counts towards the badge - the reputation cap has absolutely nothing to do with the badge. Downvotes do not count against you for a day; the badge script ignores all negative events for the day when determining your eligibility. The badge progress tracker is sometimes temporarily incorrect because it only looks at upvotes (absolutely nothing else) when tracking your progress for the current day, but will eventually update when it recalculates your number of days again. As an example, a +200 bounty award will instantly hit the mark for that day with no votes whatsoever, but will show as a progress of 0 during that day and increment later on.
However, it's also important to realize that simply hitting the mark for the day is not permanent. You can still lose the day if votes for the day get retracted later on, because a user removes their upvote, the serial scripts kills a bunch of them, or a chunk of that reputation is lost due to the post being deleted. The number of days you've hit the cap is recalculated every time the badge script checks. There is not an imaginary number behind the scenes counting how many times you've simply hit the number.