Welcome aboard.
There was a recent thread about someone who had used Zone Minder in Ubuntu 8.04. When he upgraded to Ubuntu 10 the Zone Minder software broke. He ended up going back to Ubuntu 8.04.
Just a word to the wise. Upgrading a working system can be a bad idea so don't even think about doing that on a production system.
Now as to your situation, I suspect that you may need to use a remote desktop type of application to view the cameras. There are several to choose from in Ubuntu. The one that is installed by default in my Ubuntu 10.04 system is called Terminal Server Client. Others have names like rdp and vnc. Look in the menu labeled "Applications" under "Internet" or "Network". These remote desktop clients work just like remote desktop in Windows so you have a reference. You will need to know the network address of the thin clients in order to connect to them. You will also have to know the name of a user account and a password to log in to these machines over the network.
I hope that you find Ubuntu Linux enjoyable. If you get this working then the company might delay changing these machines to Windows indefinitely. That would save them time and money.
One of the things that you may find appealing is the huge selection of free professional grade software available through the software package manager. In Ubuntu this is called the Synaptics Package Manager.
Let us know how you progress with this camera situation. If you have problems please supply enough details so that we can understand what you have done and what happened as a result.