Slow injection of non-wetting fluids (drainage) and strongly wetting fluids (strong imbibition) into porous media are two contrasting processes in many respects: the former must be forced into the pore space, while the latter imbibe spontaneously; the former occupy pore bodies, while the latter coat crevices and corners. These two processes also produce distinctly different displacement patterns. However, both processes evolve via a series of avalanche-like invasion events punctuated by quiescent periods. Here, we show that, despite their mechanistic differences, avalanches in strong imbibition exhibit all the features of self-organized criticality previously documented for drainage, including the correlation scaling describing the space-time statistics of invasion at the pore scale.