The big difference from camping in the Alps is humidity. Nights at 1,800-2,600m stay cool (5-12°C in the southern winter, 0°C on the summit of Piton des Neiges in July), but the constant humidity and the showers that build over the mountains mean you need good waterproofing and good ventilation to avoid condensation. Add to that the wind, which often picks up in the highlands in the late afternoon.
This page compares the five main types of tent suited to Reunion Island (dome, tunnel, ultralight mid, 3-person family, 4-season), explains six key technical features, lists bivouac spots and how windy they get, and gives my recommendation for a first tent.
Many locals buy their gear online from camping specialists. For 3-person models in particular, see the range of 3-person tents on tentes-materiel-camping.com, handy for a family bivouac at the Plaine des Sables or Piton de l'Eau.