Ok, I see that what I have been saying is correct. The reversing relay you linked has two momentary pulsed coils. To reverse, you must pulse the two coils alternatively. You would have to build a "toggle" to go between the timer output and the two coils. It is up to the toggle to produce the two alternating momentary pulses for the two coils.
In the
toggle made from relays that I linked to, there is no reason that you have to use a momentary push-button. That contact could come from the timer, instead...
I just downloaded the timer data sheet. It does NOT have two alternating outputs.