As you said yourself about the containment device, it’s fictional. Such a device could not be made that size. However, if it did exist…
Hydrogen bombs and other fusion devices, theoretical and real, work based on their geometry. Some effect causes matter to become massively compressed, triggering fusion, which releases energy. This can either be absorbed, yielding heat which can be converted into electricity, or released, giving a bomb.
In prospective fusion reactors, flowing plasma in a strong magnetic field compresses itself. In a hydrogen bomb a traditional thermonuclear is exploded around hydrogen isotopes, compressing them and triggering fusion.
Here, you would get some fusion, but the hydrogen isotopes you’ve included are pretty irrelevant. As matter makes contact with the surface or your nugget of antimatter, massive amounts of energy are released as one annihilates the other. This compresses the antimatter itself. With enough (and a milligram easily would be), that is what gets fused. However, the energy released by fusion is likely to be quite insignifcant compared to that from the annihilation.
A search on Google found http://www.angelfire.com/on2/daviddarling/antimatterprop.htm, which gives some figures (which I haven’t checked). This suggests a couple of orders of magnitude difference in the energies released, without considering that not all the antimatter will undergo fusion.