I manage a couple Draper rotating single-layer OHs for local schools. We rebuilt one the other day. After cleaning, we added new frames of comb, bees, new queen, lots of eggs and wet larvae. As we rolled in back inside, the bees became a little agitated. Within a couple hours they were flying around everywhere outside and running all over inside the hive. I suggested to the school that they cover the hive to keep much of the light. They did and soon the bees had calmed down and were behaving normally with no scampering all round inside and out. Is it best to keep them covered until there is a class present who needs to make observations? Then cover again when the class is over?
It sounds like the light triggered orientation flights which is normal. Covering it helps them maintain proper brood rearing temperature. If it is in a window getting direct sunlight, then you would need to cover it to keep it from becoming a giant wax melter and to keep them from flying during cold weather in winter. If it is not getting direct sun and the bees are able to raise brood, then you don't need to cover it all the time. But, I keep mine covered because it doesn't hurt to cover them when no one is looking at them and makes things easier for them.
When I had mine at the garden center where I work, when the hive first gets installed, we keep the sides covered for about 3 days as the bees get used to where the entrance is at. After that, they don't run around the inside all crazy like, but we do cover them in the evening when we go home. Not sure that we have to do that though.