Unusual behavior when controlling a Button Matrix
The question is: how are you "controlling" the wires using an arduino? The microcontroller is probably pulling the rows (or columns) up (or down) one at a time, an then checking the voltage on the other axis to detect button presses in that row/column.

To emulate this using an arduino, you would have to monitor the energized axis, and then output to the sensing axis in a synchronized fashion. Depending on how the unknown microcontroller is programmed, this may be very difficult, because it could read very soon after energizing. Perhaps too fast for your arduino to react.

It's also worth noting that other arrangements exist besides row/column. Are you sure this is how the keypad is arranged?