Do the files have normal names? Or is a dot preceding like .filename.indd?
If this is the case, they are trying to open the wrong files. The Mac is creating such files automatically, they are invisible on the Mac, but visible on other computers.
It writes two files. One is ._Filename which is hidden automatically, but also the regular "filename" is being written as hidden as well. I work with OP we're not sure whats going on. Even with a clean install of Yosemite, and Adobe apps same issue is happening.
What spec and OS is your server running? Do you have a RAID attached? How is the RAID/Storage formatted on your server.
The ._Filename file is indicating that it is a Windows server of some description. We have 2 Mac servers, 2 Redhat Linux servers and several Windows servers at work so I can maybe duplicate your working environment which may lead to a solution.