If you are in any way uncomfortable with working with this, PLEASE FOR YOUR SAFETY hire a qualified, licensed electrician to do this job!!! If it is done wrong, you can kill someone all too easily with the voltages and currents involved.
What you described is normal in some circumstances.
That said, Do you have a test light or multimeter?
Your description leads me to believe you have 230V on a black and red pair, and 115 on the remaining black and white pair coming from your breaker box. I will assume that the GE timer had a 115V timer motor, needing the extra wires. You will need to figure out which black goes with the red and which black goes with the white. You are correct that the green is ground.
From the breaker box....
In the breaker box, one of the black wires will be paired with the red, and connected to a two pole breaker. The other black will be connected to a single pole breaker. The white will be connected to a neutral bus bar, with several more white wires from other circuits. The green wire will be connected to a ground bus bar, which depending on your location, may be bonded (wired) to the neutral, as well.
You can see now why you need to have a tester to be sure you have each black wire paired properly. If you don't, you will not have any protection on either circuit.
The wires to your motor....
While it is allowed to use the white for the second wire in a 230V pair, the original electrician should have marked it with either red or black tape/paint.
Connections in your Intermatic....
The green wire from both the breaker box and the pump will need to go to the green screw (should be on the far left in the timer). The red wire from the breaker box will go to terminal 1. The black that is paired to it will go to terminal 3. The white wire from your pump will go to terminal 2, and the black to terminal 4.
The extra black and white pair from your breaker box will need to be isolated from any other connections in the timer box, or removed completely. If removal is not possible, cut the bare wire off at the point it is stripped of it's insulation. Make sure the white and black wires are of different lengths. Fold them back onto themselves individually, and wrap each one with black electrician's tape. Make a tag or label for your single pole breaker that this pair's black wire connects to as a reminder that it is to remain OFF.