I would feed them it in the morrning.. No link stating the facts for you, just a bit of experience
Like previously mentioned feeding them at night is a waste. Aside from risking rot & promoting the habitat of Fungus Gnats - Plants process the water & nutrients when the lights are on and turn it into energy. They only do it when the lights are on as the need to recieve the light to do it (part of the photosynthesis process, it cant be done in the absence of light).
The night time however is the time when the plant uses all it's energy that it has been storing throughout the day & does it's thing.
So in answer to ur question i think the roots grow all day, & primarily @ night - tho i would still feed them the root excelerator in the morning!