I have one like yours (Acerola, malpighia glabra), but never had this "things" growing on it.
IF it helps, some common pests and diseases that can occur in Malphigias:
"One of the major obstacles to successful cultivation of the Barbados cherry is the tree's susceptibility to the root-knot nematode, Meloidogyne incognita var. acrita, especially in sandy acid soils. Soil fumigation, mulching and regular irrigation will help to keep this problem under control. The burrowing nematode, Radopholus similis, is also a cause of decline in otherwise healthy trees.
In Florida, the foliage is attacked by wax scale, Florida mango scale, and other scale insects, whiteflies, a leaf roller, and aphids. In Guatemala, the aphid, Aphis spiraecola, attacks the leaves and young, tender branches. This pest and the Hesperid caterpillar, Ephyriades arcas, require chemical control. In Puerto Rico, the tree is often damaged by the blue chrysomelid of acerola, Leucocera laevicollis. Some fruits may be malformed but not otherwise affected by the sting of stinkbugs. None of these predators is of any great importance.
The major pest in Florida is the Caribbean fruit fly, Anastrepha suspensa, which seems to attack all but very sour fruits and the larvae are commonly found inside. In Guatemala, a fruit worm, Anthonomus florus, deposits its eggs in the floral ovary and also in the fruits; the larvae feed in the fruits causing deformity and total ruin. Drastic control measures have been employed against this predator, including the incineration of all fallen, infested fruits and the elimination of all related species that serve as hosts.
Few diseases have been reported. However, in Florida, there are cases of anthracnose caused by Colletotrichum gloeosporioides, and leafspotting by the fungus, Cercospora bunchosiae, is a serious malady in Florida, Puerto Rico and Hawaii. Green scurf, identified with the alga, Cephaleuros virescens, occurs in Puerto Rico."