I have reported and discussed the problem on Git.
It turned out that everything works correctly and in the end it is just an operation- and display-problem.
When assigning a package to a group, it says '1 computer successfully assigned' because a group is considered as a machine (a group is registered like a machine on the hardware table).
That means when it says '1 computer successfully assigned' it actually means '1 group successfully assigned'.
The packages do not appear directly in the deploy area (under the menu item 'Deployment') of the corresponding machines, but first in the deploy area (under the menu item 'ACTIVATED PACKAGES') of the respective group.
Only when the machine contacts the OCS server the next time (e.g. for the daily inventory), the machine gets to know that there is a deploy for it.
Only from this point on the package is in the deploy area of the machine.
I had tested this after the explanation and it behaves exactly as described and therefore correctly.
This here only as info, for all which stand before the same 'problem'.
Source and more info:
Many greetings and thanks.