So here's the picture, an island about the size of Sicily is on its own tectonic plate, it borders three other tectonic plates, it's separating from all of them at the exact same time. This is a fantasy setting but I don't want "because magic" to be the only answer, so please tell me if this is scientifically possible. To clarify, plates directly neighboring the small plate are moving away from the small plate, at the same time the small plate is scrunching up.
Not in the sense that you may be thinking.
You may be thinking of something like our own Antarctic plate, for example. It is subducting somewhat beneath South America, but other than that, the whole of its boundaries are either transform or, specially, divergent faults - which means that overall, its movement away from other plates (from its point of view) is much larger than its movement towards South America.
A divergent boundary happens when plates are moving away from each other. However, this does not mean that the plates are actually separating. They grow bigger around their boundaries. This will not expose mantle. According to the wiki on divergent boundaries:
Divergent boundaries within continents initially produce rifts which eventually become rift valleys. Most active divergent plate boundaries occur between oceanic plates and exist as mid-oceanic ridges (...)
... Which might be the dominant feature on the seafloor around your island. It will probably be surrounded by ocean ridges which are sure to have hydrothermal vents.
But your tectonic plate will always keep the same distance from the other plates.
I have edited the answer to include Jaycie's comment:
The Antarctic Plate is that the plates surrounding it are moving away from it from its point of view. This way of describing plate motion, as relative to another plate, is pretty standard. From the point of view of the African Plate, Antarctica is moving toward the Pacific Plate but the Pacific Plate is moving in a similar direction roughly twice as fast, so Antarctica can't catch up.
Growing smaller somehow so it pulls away from the surrounding plates?
It a plate would begin to "shrink" somehow, the mantle of the Earth would be exposed, its top layer begin to cool, and form a new section of the Earth's crust. So too if a section of the crust rose upwards or simply vanished.
I expect that sudden exposure of the mantle would likely be quite violent - water on the surface would likely begin to spill into the exposed mantle, generating superheated steam.
Yes, this is possible. Tectonic plates are moving in seemingly random patterns, colliding or separating from each other. When the plates collide, their boundary is called "convergent". When they are moving apart, they called "divergent" (not to be confused with popular YA series). Sometimes, the plates can be completely divergent, meaning that all their neighbors are moving away from them. The real world examples of such are East Africa and Iceland.