Example of red on flip flop
Adding to your point, the latest version(s) of Photoshop you should definitely use the Adobe utility to print a chart without correction, that's why they made is as people were complaining that do profiling once they took out the means of truly turning all color management off in PS, starting at CS5.NO!
You use no colour management of any kind to print the test charts, to get an accurate measurement of what the printer/inks are doing without any adjustment, ideally using the Adobe Color Printer utility which has no options for colour management for this purpose.
Once you are using the created ICC, you need to keep all colour management off in the printer driver, and keep the print quality and media settings the same.
In Photoshop, you should use Adobe RGB 1998 as your workspace, and for printing set it to Photoshop manages colours, and select the new ICC you've had made.