No both outputs of the original transformer are not 24 volts.
Look at page 6 of the manual.
Yellow is the common terminal for both voltages.
Red is the 9.5 Volt Hot.
Blue is the 24.5 Volt Hot.
So for the 24.5 volts. Use the Yellow Common and the Blue 24.5 Volts Hot.
The Red 9.5 Volts Hot is not used. Tape it up so it doesn't touch something and short out.
The Rain8II manual 30004 {I looked at the expansion set module kit} shows the 24 volts on terminals 11 and 12. So connect the transformer there.
The 30005 starter kit manual doesn't call out the 11 and 12 but it should be the same.
The Common terminals on the Rain8II are for one side of every valve in use.
Don't connect the transformer to one of the common Rain8II terminals.
Use 11 and 12 for the 24 volts. Your choice on colors. Just get the Yellow and Blue wires connected to 11 and 12 of the Rain8II.