2014 Avalon Limited
The message center of your Hybrid is different from my gas model and my display is different from the XLE but....when in ECO mode my message center gets a green bar and eco is shown at the top. When in NORM mode nothing is displayed, when in SPORT mode the display gets a red bar, "Sport Mode" is shown for a few seconds on the display and the word 'sport' displays near the headlight on icon.When I press Ev, Eco or Sport nothing happens , the instrument panel only shows Eco
Check your display again and see if there's a color bar or "sport" is displayed someplace when in that mode. Start button needs to be pressed twice or start (whatever it's called with hybrids) the car.
Another thought, check the Avalon Hybrid forum to see if you can get a more definitive answer.