A Note About Ground
TDT digital signals use an active voltage and ground. Any third-party device will also have a ground line that needs to connect to the TDT ground, otherwise the two systems will be 'floating' with respect to one another and there could be a large enough voltage difference between each system to create false TTL signals.
Think about this like a trampoline - if you and your friends are jumping on the same surface, then you know how high you are with respect to one another. But if one of you was on the earth and the other was on an elevated trampoline, then there is already a height difference between you two. When the person on the earth jumps, they need to go much higher in order to be 'above' the trampoline. When the person on the trampoline jumps, they don't need to go as far before they reach a large absolute difference in height between themselves and their friend.
If you are using a BNC cable on both ends, then the ground is on the BNC shell and you don't need to worry about manually making the ground connection.
If you have a BNC on one end (usually the TDT side) and flying leads on the other (usually the third-party equipment side), then be sure to connect the negative side of the flying leads (usually green or black colored wire) to the third-party ground port. The red lead is your active signal.
If you are connecting a DB25 cable or individual wires to the TDT digital IO port DB25 connector, be sure to use pin 5 on the TDT side as a common ground for all your devices. If you have one third-party device, its ground must connect to pin 5 on the TDT DB25 connector. If you have multiple third party devices, they all must connect to pin 5.
You can find DB25 to terminal screw port adapters that are very helpful if you are connecting multiple bare wires to the DB25. Google "DB25 D-sub Male Adapter Plate RS232 to Terminal Signal Module Breakout Board"