You can watch every step of this unfold, with explanations as it goes, here:
https://fivethirtyeight.com/live-blog/2020-election-results-coverage/No votes "magically" appeared over night. No vote batch went "100%" for anyone.
There were three types of votes being counted: 1) mailed votes, 2) Drop-Off votes, and 3) In-Person votes. In these three, there were variations, like "early in-person vote" vs "Election day in-person vote" or even "Early drop-off vote" vs "election-day drop-off vote". Because of the nature of the campaigns, in general Democrats tended to vote early, and Republicans tended to vote on election day.
So when counting, if the batch was "early" with either drop-off or mail-in, it tended to go Biden. And if the vote was "election-day" with either drop-off or in-person, it tended to go Trump.
Then of course you have the variation on geography. Votes in Philadelphia go very strong Biden, while votes in rural areas go very strong Trump. So WHERE the votes came from in a particular batch is important to what the vote is likely to be.
So then you come to any moment in time where you think some "magical batch of mystery votes" is being counted. If the batch is both 1) from an urban location like Philadelphia, and 2) a batch of early mail-in or early drop-off votes, it's going to skew extremely hard to Biden. On the other handm if the batch is both 1) from a rural location, and 2) a batch of election-day drop-off or in-person votes, it's going to skew extremely hard for Trump.
Ther blog covers just about every batch of new counts, in all the states people are watching. Not one has been particularly remarkable in the count. They predict what it will be and generally speaking it's coming in roughly close to their prediction. Which isn't magic, this is a simple formula which is baring out over the election in all the states.
If if you were not watching as it happened, if you just got blips here and there, or partisan spins on what was happening, I can see how people would think this is all some big nefarious fraud. But it's not. It's actually quite boring, and nothing nefarious is going on other than some minor human error here and there. It's just a lot of tired poll workers counting every ballot coming in. There are MANY Republicans involved in every poll counting facility in all the states in question, even in urban counting districts. It's mandated by law that you have a minimum of one member of each party (and then usually two independents) present for any issues. They're not reporting any major issues in the count.
As for the number of people voting, it's up for both Republicans and Democrats and not just one. It's up dramatically, for both parties. Trump received the most number of votes of any Republican, ever in the history of the nation. Biden received the most number of votes of any Democrat, ever in the history of the nation. Voting, across the board, is way up. This should come as no surprise to anyone, because it's SUPER EASY TO VOTE THIS TIME. Because in many states EVERY registered voter got a mail-in ballot which could also usually be dropped off in advance of election day. That's atypical. It gives people a lot more time to get their ballot in and lot more locations to get their ballot in and fewer restrictions on the day of the week or the time of the day they drop their ballot off. This level of flexibility increases the turn-out dramatically. And it's increasing the turnout for both major parties and not just one.