You shouldn't need a common ground between systems. In fact, many times the ground of the DMX cable is lifted on one end so as to not have a group loop in theaters. The beauty of RS485 is that it's a differential signalling method, and the receiver is looking at the difference between A and B, not necessarily relative to earth ground.
If the cheap 3 channel controller isn't using a standard interface chip, such as the ones used on a number of the DIY controllers, then it may not be following the spec as it should...
Where did you get the cheap 3 channel DMX controller? Sounds like one to avoid!
"Beam me up Scotty, there are only limited pockets of intelligent life on this planet!!"
Communicating humor in a text only medium is an art form subject to imprecise interpretation by the audience...