Hi, missruth. Welcome to the forum.
When I created Chihuahua, way back in 2005, it did indeed operate as you surmise. However, from time to time there were problems because of server outages, network outages, server overload, etc. This caused situations where people couldn't play when they wanted to, or when they could play but their words weren't going onto the scoreboard. So over the years I've implemented a few measures to improve reliability, including use of local storage in the player's browser.
Now, daily puzzles are actually created a few days in advance - by random selection from a list of seed words, as you say. Some details of these future puzzles are stored by the player's browser. So when it's time for the new 10-letter puzzle to start, you can play it, even if the server has crashed, or your internet is on the blink, or whatever. The words you've played will be stored on your device, and submitted to the scoreboard the next time you're back online.
This arrangement inevitably opens up some vulnerabilities, which I'd prefer not to discuss in detail. But I feel it's better to try to ensure constant availability than worry too much about the possibility of someone who can be bothered to work out how to crack the system. Playing a puzzle before it's meant to be open could perhaps occur inadvertently, as you suggest. Imagine someone who frequently moves between time zones and doesn't bother to reset the time zone on their laptop or tablet. Suppose also that this device is only intermittently connected to the internet, because it's reliant on wifi. (Incidentally, I wonder what ppilot's occupation is.)
Hopefully you can get some sleep now.