The foam surrounding the fullerene is highly electronegative and bonds strongly with the carbon shell of the fullerene molecule, creating an electron deficient internal environment which suspends the antimatter; preventing 'accidental' reactions with the fullerene shell. Despite how it may seem, most of the structural strength of the fullerene molecule is provided by the foam itself; the fullerene provides the symmetry necessary to suspend the antimatter evenly within the cage.
The foam itself is very robust, with foam molecules bonding with the fullerene even if the material reaches 10's of thousands of degrees (the fuel can become a partial plasma, but the foam sticks to the fullerene still). So in order to release the antimatter an intermediary fusion process (using the heavy hydrogen isotope) is required to raise the temperature of the foam to a point at which the foam fails and the fullerene cage cracks open to release the antimatter to react with whatever unfortunate matter happens to be wandering by at the time.
So it should be pretty stable; unlikely to detonate even if the ship it is contained in suddenly was to be destroyed.
In summary, fullerene is the eggshell, the antimatter the yolk; the foam the egg carton and the isotope of hydrogen a rather large heavy implement for making a big mess of your kitchen
