Erosion is not your friend, and stuff gets scarce
The answer to your question depends heavily on when the continents were lifted. If they were lifted after humanity evolved and spread, you'd see a very different result than if they were lifted when the dinosaurs roamed the Earth.
Scarcity
Your floating continents are only so thick, and if there is land below, perhaps they aren't continent-sized but instead country-sized. There are no oceans to fish, no oil fields to drill, and few if any volcanic minerals. You won't have coal or diamonds, and you'll probably have very little metal in general if the islands are as thin as those in the picture. Water will also be a precious resource gathered every time it rains, since any lake or river falling off the island essentially drains away.
Weather
The temperature of islands is still dependent on latitude; polar islands are cold, equatorial islands are hot. You'll lose many of the effects of living near the ocean, such as increased precipitation and moderate temperatures. Depending on the height of the islands, you may see them get very cold at very high altitudes - anticipate snow-capped mountains. Rainfall is also altitude-dependent, but I think it's safe to say your islands can get rain. My biggest concern is the effect of rain on geology.
Geology
Weather erodes terrain. Over millennia, rain reshapes landscapes; over eons, it levels mountains. If your continents aren't restored from underneath (read: plate tectonics + volcanism) the dirt will basically slide of the edges. 155
This is bad news for your already resource-poor islands. This type of geology might make for some interesting features, though. Whole islands may calve and split like icebergs as they erode. I would also worry about erosion from underneath - condensation on the underside of the islands may create some gorgeous stalactites hanging down, but it will also eat away at the land.
Evolution
This topic is entirely dependent on how long ago your islands were lifted. On Earth, we see similar species on different continents (ex. American possums vs African possums) due to continental drift. We also see similar species because they crossed the ocean (ex. Galapagos tortoises vs those in continental South America) and sometimes even the same species on different continents (ex. humans). If each continent is totally geographically isolated, your species will likely evolve divergently faster, since their populations won't mix. Birds will be the only mechanism for spreading species (which is how some man-made ponds get fish in them!). 445