These corals can easily be trained to come out during the day and have no issue with light (mine out out there under 2 x250w MH's). In the wild they often live under overhangs at the entrance to caves, not because they enjoy the dark but instead because water tends to flow briskly through these areas and that makes them a prime location to capture food.
If you want to train your coral to open during the day you need to be consistent about what time you are feeding it each day.
The coral will catch on in a short time.
..and btw, even with mine opening during the day, they also do open up at night.
You only need put a small amount of food into the tank about 10 minutes before you want to feed while training. I used cyclopeeze. Not so sure about using mysis 'juice' since that has a unwanted pollutents in it...
I also spot feed each head daily with my baster filled with mysis and have had much success with them mulitplying.
Just a suggestion - if you are turning off any pumps to feed them (I don't)..make use of an egg timer so that you remember to turn your pumps back on!!
Some folks have problems with their other fish & shrimp stealing the food from their sun corals..my Purple Tangs favorite entertainment. You can cut the top 4 or 5 inches off a plastic soda bottle & hot
glue a few marbles on the outside to weigh it down, and pop that over the sun corals until they are finished eating.