I checked the factory service manual for a 1997 Avalon, and pressures at the test port range from 58~66 PSI in drive at idle to as high as 269 PSI in reverse at stall speed. Of course, that kind of pressure does not travel down the hoses to the transmission cooler, and a look at the transmission oil pan will tell you that it is not designed to handle that kind of pressure. There is no specification published for transmission cooler line pressure. My guess is around 20 ~ 30 PSI.
Unless you have totally botched the hose installation, it shouldn't fail catastrophically and will leak before it pops off so just keep an eye out for leaks.