First I note: Catching At fluid before coolers, leaves old AT fluid in coolers. I catch further downstream, getting the most old out.
Yes your pink circle is coming from AT to pre cooler/warmer, if nobody switched factory routing.
It then goes into the pre cooler/warmer in bottom of engine radiator within bottom plastics. Comes out your blue of PS LWR rad side. Then goes to front AT fluid radiator. Which is smallest radiator of the 3 (engine, AC condenser & AT fluid rads), behind grill. It then comes out AT fluid radiator, and heads back to AT.
BTW: here's, the small pre cooler for AT fluid, removed bottom of engine radiator.
forum.ih8mud.com
Blue line is fluid flow out of AT. Red line is return to AT. Red arrow is return pipe, where I attach catch hose. We can add AT fluid to the hose we pull off this return pipe. Shops using a fluid exchange machine, spliced in at red arrow also.
I like to catch AT fluid, after passing both coolers/radiators, at return pipe next to top side of radiator on PS. Note picture below is of 98-02. Starting in 2003, Toyota routed power steering to a cooler in front of radiators also. So above transmission in & out pipes/hoses. We'll see two more pipes/hoses for power steering (PS)
98-02 AT fluid to/from cooler pipe/hose configuration. The 03-up will have two more pipes/hoses above these transmission pipes/hoses, which for PS.