Thanks to all for helping!
In fact, it works, this is how to do:
The Alternate Data Streams support must be configured on a per share base, not as an general option.
This means, the options have to go into the OMV->SMB/CIFS->Shares->Extra Options
There, you have to possibilities:
a) Streams depot
Allows to have ADS of any size. The ADS will be stored in a separate directory. I recommend to point this directory somewhere to your data disks, not to the system disk. The settings would be:
vfs objects = acl_xattr streams_depot
streams_depot:directory = /media/xxx/samba/.streams_depot
(this is an example directory path)
b) XATTR
There the ADS will be stored as extended attributes, i.e. they are limited in size (I am unsure about the max. size, somewhere I read about 64 kB), Configuration (Again put it into Extra options of the Share definition):
-> I haven't tested this version, it could be that this doesn't work - see the comment of ryecoaaron who mentioned a kernel oplock problem
NB: The acl_xattr is optional, if set, you get extended ACL-Support, to be honest, I am not 100 % sure if this is really necessary