Discrepancy between score page kills and tour stats.

[Skyyr]

When a tour resets later than 12:00 AM on the first day of the month, the pilot scores page will log all kills under a plane type for the next tour, instead of for the current tour.

For example, if the scores reset on May 4th (instead of May 1st) and I fly until May 3rd in a P-51, all of my P-51 kills are logged under next tour's kills breakdown by plane type.

You can see this when the tour updates by going to player scores and pulling the player scores for the new tour. On the score page, click the "Kills" link and you'll see that any kills gained from the start of the month are applied to the current tour, instead of to the previous tour where they belong. You will see the kills for the P-51 logged under Days 1-7 for the current tour, instead of under Days 28 and up for the previous tour.

[Copprhed]

Kills after the end of the month, whatever day it is, SHOULD be on the next tour, as tours begin on the first of each month. Most of us realized it a long time ago. No big deal, because it's accurate.

[Lusche]

Kills after the end of the month, whatever day it is, SHOULD be on the next tour, as tours begin on the first of each month.

Not always.
They begin on the date Skuzzy does the tour reset, which may not be the first of a month. Weekends or holidays postpone this reset. 

[Skyyr]

Kills after the end of the month, whatever day it is, SHOULD be on the next tour, as tours begin on the first of each month. Most of us realized it a long time ago. No big deal, because it's accurate.

Right, but the issue is that those kills aren't logged under the correct tour. Using my original example, if I kill 300 more aircraft from May 1-3, but Skuzzy doesn't reset the tour until the 4th, they will be attributed to May's tour on the Score page, even though they're actually logged in-game under the April tour.

What you end up with is the Kills breakdown page being inaccurate.

[Skuzzy]

Yes, kills do not start counting towards the next tour until the actual reset is accomplished.  If I do not manage to get the new tour kicked off before the ranker runs, then I run the ranker manually after all the arenas are reset.  This 'closes' out the old tour with a final ranking.

The start and end dates do not mean anything.  The time of day has nothing to do with it.

Scores are tallied at the end of each sortie into whatever is the active tour database.
Ranks are calculated once a day, from the active tour database.

Basically, for your purposes, all the start of a new tour does is reset the kills, scores, and ranks to zero.  All the ranks are accurate, all the scores are accurate.   None of which depend on a date or a time.