Hello, welcome to Bonsai Nut!
Barbados Cherry is a tropical shrub to small tree. Outdoors in the tropics they like full sun to part shade. Indoors this would translate to as bright as you can give them, since a glass window pane cuts out nearly 50% of the sun that hits the window. So indoors is already lower light. The CFL lamps are okay, but not the best, good enough for now. One way to help is to use an 18 hour day length. This helps to make up for the lower intensity of the CFL's. More than 18 hours of light is wasting electricity, but lights on up to 18 hours per day there is measurable improvement.
Looking at what your Barbados cherry is potted in, it is hard to tell. Feel the surface of the gravel. If it has been glued into place (stores do this for neatness, no dirt spills) you need to peel off the glued on layer so the roots can breathe and you can get better control of watering. If a lot of soil comes with, replace it using gravel of about the same size grains, aquarium gravel will work short term. You can re-pot your tree later in the year, after it has had a chance to grow out a bit and recover from transit from nursery, then shipping, then life in the store or storage somewhere then to your home.
To tell when to water, stick your finger into the potting mix, if it feels barely damp, its time to water, if it is bone dry, you should have watered a day sooner. You will see a pattern, but don't put the tree on a schedule, because it will vary depending on temperature, relative humidity, and light. So it may normally need water every 3rd day, but it could vary several days either way as weather varies. If the soil has a lot of peat in it, it might need watering only once a week. You will need to figure out the pattern, so you need to check it at least once a day, but only water it if the soil has become almost, but not quite dry.
I think your leaves yellowing are related to the glued on gravel. Once you get rid of that, your tree should improve. There is a search function on this website, use it to look up discussions of Barbados Cherry, also search the genus name for this tree, Malpighea or on the full species name Malpighia glabra or Malpighia emarginata. All 3 searches will lead you to threads about your tree species. (different threads may pop up for each search term) The current correct scientific name is Malpighia emarginata, a recent name change, most literature called it by its older name, Malpighia glabra. The way to tell them apart, the true M. emarginata has a fruit that tastes good, the true M. glabra has a bad tasting fruit. (insipid flavor is the term used by Wikipedia). The exact name is not too important, everyone pretty much knows which plant you mean when you use "Barbados cherry".
Welcome to the forum. - Leo
