thank you for your answer. The problem exists much longer than 12h and Sync Attributes had no effect. But while I was checking your idea, I found rather incidentally a solution that solves it all.
The group I want to add from AD into WS1 has to be an universal group. A global group doesn't work.
Is that a bug or a feature? I've never read about it, but I tested a universal group and it works fine. All users are automatically added into WS1, just by adding the AD group. Exactly what I was looking for.