Engine water flow for trans cooler

[gm4106]

Trying to think out the water flow from the motor to the transmission cooler. The pictures 1 and 2 is the water flow of the motor on a 8V71 gm bus motor. I would think it flows that way. The transmission to cooler PDF files shows the water pump end as a return and receiving from the block. It shows the arrows going towards the water pump, Thinking that would be the return. Only the water cooling part not the transmission lines. Is this true that the water pump is the return?

[gm4106]

picture 2

[gm4106]

PDF file