hi-biscus = high-light
Hibiscus need really high levels of light to thrive. I don't know where you live (Florida?) but in Northern California the have to be right in a window that gets a half a day of unobstructed sun to grow well. You can grow them under fluorescent lights if the tubes are strong ones and the plants are close enough to the tubes.
Rotating plants in and out of the light generally does not work. It takes the plants more than a week to recover from a week in the dark.
Maybe if you had multiple plants (I'm thinking 5 or 6), and kept the cage well-lit, they wouldn't be set back to much by the rotation.
And be sure to feed your hibiscus well. They need a lot of food to perform and flower in a pot.