[cappuccino]

My lecture notes says that in fullerenes (C₆₀) there are localised double bonds which makes them undergo addition reactions. But weren't fullerenes supposed to be unreactive which is why some molecules/atoms can be stored safely inside them?

[Roentgenium]

It is indeed very hard to make a fullerene undergo an addition reaction due to the very large conjugated system that is created. Although double bonds stay double bonds which give them an excess of electrons, and in turn make them viable for addition.
The storing of molecules in fullerene is some really advances technology and has little to do with the reactivity of the double bonds in a conjugated system. afterall, a completely non-polar unreactive molecule would have no effect on double bonds where, for example, bromide does.