That’s oversimplified. Some agencies continue to operate for a bit because they have enough money stashed to do so. For example, the Smithsonian stayed open over the weekend and is apparently open today as well. The EPA will stay open for another week because they apparently have a nice chunk of cash somewhere. The postal service will operate indefinitely because they earn their own money.

For everybody else, a shutdown means you stop working right away. For most people that means the first day they’re affected is Monday because most of them have the weekend off, but people who would work on the weekend have already been affected. There’s no room for a bureaucratic delay or people failing to get the news. I’m pretty sure it’s illegal for non-essential people to work during the shutdown unless their job is somehow still funded. Anyone who went to bed early on Friday and went to work on Saturday without checking the news would be told to go home.

The bureaucratic prep for a potential shutdown (including identification of essential personnel and functions that are exempt) usually happens in advance; if you missed the memo and you aren't exempt, the whole “not being allowed to work” thing will catch you up on the key relevant bits for you right quick.

> In German radio news, the US correspondent explained that the weekend should still be fine, with full effects of the shutdown beginning around Monday with the new week

That's just a way of saying most (but not all) non-essential functions run on a normal workweek, so are effectively mostly “shutdown” on the weekend anyway.

But that was because few people work on the weekend anyway. Anyone affected working on the weekend knew that they wouldn't get paid.

> with full effects of the shutdown beginning around Monday with the new week.

That's just because most government services are always off on the weekend, not because of a delay. The news was distributed widely and broadly near instantly.