I wonder if your question about "when the day starts" has anything to do with permissible hunting hours... when is sunrise and when is sunset?
I examined that question of "what time or date is it where?" quite a while ago and in looking at the maps, it appeared that many "aberrations" in the "International Date Line" as well as "Time Zones" were
merely matters of mutually-agreed-upon practicality in terms of commerce and culture.
We humans built the time system for the world, and there is no external or cosmic authority to simply say, "The International Date Line is at exactly 180° of Longitude, like it or not, and go fly a kite if it happens to go through your living room."
As touched on above, there are even "islands" of areas on one side of 180° which actually consider their dates to be on the opposite side of the arbitrary 180° demarcation line. This, once again, is dictated by commerce and culture and the choice of the inhabitants.
To illustrate this arbitrariness with an example slightly away from the "International Date Line" problem, I submit the following:
As it happens, Denver, at 105° West Longitude, is exactly on one of the "15° per hour" lines. Yet, arbitrarily, without appeal to cosmic authority, it is the same time as it is in Denver for many miles in either direction from 105° W longitude:

You will note that even though there are 15° of the earth's rotation per solar hour (360° divided by 24 hours), up in the far northern reaches of Canada, this time zone runs from about 86° W to about 140° W, which amounts to about (140 - 86) = 54° of longitude.
This amounts, in turn, to 54°/15°(rotation per hour) = 3.6 hours total of solar time. In other words, you can be as much as +/- 1.8 hours away from true solar time in those upper reaches of Canada.
Wow.
You will also note the rather glaring disjunct between the time zones for Edmonton, Alberta Province, Canada, and Winnepeg, Manitoba Province, Canada, compared to the corresponding United States time zones. Hey, Albertans and Manitobans didn't like the way the US set it up. So what can you do, sue them?
Well, whatever works for the inhabitants of that time zone. It's all arbitrary anyhow.
After all, at the North and South poles, neither time zones nor the International Date Line have any meaning at all. Lucky for penguins who are waiting for the 5 o'clock "happy hour,"eh? It's "happy hour" all the time ! Woo-hoo !
Terry, 230RN
NOTE 1: The map above is of course distorted in terms of mileage because it is a Mercator projection --as if the earth consisted of a cylinder rather than a globe.
NOTE 2: I could not get the degree symbol, ° , to work properly in all cases.