disclaimer... I'm no marine biologist...
Here is the paper that the 4 on 8 off cycle was derived from.
http://people.oregonstate.edu/~weisv/pdfs/Yacobovitch%20et%20al.%2004.pdf
If you look at the graph on the page labeled 38. You will see that peak motility of the zoox being studied occurs at about 3 hours of light exposure and then begins to fall off steeply after 4 hours.
"3. Results
3.1. Rhythmicity of algal motility
Motility of freshly isolated algae from mature colonies of H. fuscescens exhibited dielrhythmicity under a 12L:12D cycle over a 5-week period (Fig. 2). Algal motility began
0–1.2 h after the light was turned on, and became most intense 1.5–2.25 h after that time (lag time) with a peak duration of 2.5–4 h (Table 1). Peak motility period lasted 1.5–2 h.
Motility then gradually decreased and ended 3–5 h before dark. Motility duration was 7–9 h and was never observed during darkness."
Also note about constant light exposure...
"No motility occurred when algal cells were kept under continuous dark. Furthermore, no
motility occurred when algal cells were kept under continuous illumination immediately
after isolation or after initial 12L:12D cycle for 3 days and then transferred to constant light..."
While this article focuses on motility of zoox I believe the thought process is that energy levels peak around the same time period motility peaks and hence is able to maximize energy to the coral tissues.