Yes this is normal behavior for all networked files.
The recycle bin is a local and per-user listing of the files deleted.
The per-user bit does less regarding networked files. The issue with networked files is that they aren't on your computer and your recycle bin is on your computer.
I can understand not wanting to copy potentially large files over the network to your computer just because you deleted them, and then the headache of trying to deal with undeleting a networked file if you're disconnected from the network. No, actually physically moving files to a different computer when they're deleted doesn't make any sense.
However, I think it should at least be an option for the files to be placed in the recycle bin on the networked device for that particular user. I suppose the reasoning for this is that it could compromise security and network file servers really should have file backup and restore systems independent of the OS. But you'll probably find that even on the computer on which the file physically resided, the deleted files are not in the recycle bin.