The only mention of Delayed Action in my copy of the manual is on page 12:
"Characters May not move out of order, with the exception of the Delay Action command which will move a character farther down the sequence list."
There's nothing like that in ITB that I'm aware of, the closest thing is in STB by pressing space to cycle through your squad members which will move your current character to the end of the sequence list for your squad.
So either it wasn't implemented, it's a misprint in the manual and should of been mentioned under STB not ITB or they were refering to the Overwatch mode, perhaps by an earlier name?
Or perhaps they were talking about the reserve action command (Alt & Left Click) but I've used it in either Fallout or FOT so I don't know if it affects the sequence or not.