They either have a network driver for Docker and an instruction to use it, or they support standard network filesystem shares like NFS and you can use an NFS volume.
As a first step, if you search for “nfs docker” or something like that, you can find posts like this
If you need more help, please, share what your specific issue that you need help with.
Regarding the network mode, I don’t see how that is relevant for mounting a network storage.