I don't think its really a matter of the Turbastrea not caring either way. Its the Turbastrea's food source. In an established reef tank(over a year) you will see a lot more micro inverts out at night rather than the day. This stimulation causes the Turbastrea's polyps to open and feed on the oranisms swimming around. I have witnessed this activity with photosynthetic corals as well. If you were to take a turkey baster and give each head of the colony a minute puff of food at any portion of the day you should be able to come back thirty minutes later to see your Turbastrea just as open as it was at night.