Now I hop into my time machine and go back to 1:00pm, but this time, instead of placing the 1 btc bet at exactly 1:00pm, I wait a few seconds and then bet. Will the result be the same, or since some time has elapsed, will I get a different roll outcome? If you want to use a more extreme example, let's suppose I wait 10 hours after 1:00pm before placing the roll.
Is this question even definitively answerable or am I in the same territory as asking whether a god or gods exist?
On most of the provably fair gambling sites, bet results are generated by server seed, client seed and nonce. With those 3 things unchanged, the bet will have the exactly same result no matter you play it at 1 PM or 2 PM.
But i guess server seed changes from time to time, for any reason or another.
So bets made in different times, even if time is not used directly
Server seed shouldn't be changed unless you choose to change it. If the server seed changes automatically as times goes by, the site can manipulate it and cheat.