The three populations are characterised by the metal content in the molecular cloud whose collapse gave rise to the star. It doesn't directly have much to do with the age or luminosity - only the initial metal content matters (which doesn't change significantly throughout the life of a typical star in the main sequence).
Pop I stars were born late enough in the universe's history for the gas to have been enriched by earlier generations. This enrichment makes them 'metal rich'. Among every other variety, you'll find massive, bright young stars here, since these must have been born late enough not to leave the main sequence yet.
Pop II stars were born from still relatively pristine clouds of gas, hence they're 'metal poor'. You'll find older, dimmer stars in this population, since these have long enough life spans to still be around.
The hypothetical Pop III stars should be the first stars to be born, and since there was only the primordial hydrogen and helium (and some lithium) around back then, they are thus 'metal free'.Again, the fusion processes throughout the life of a star do not significantly change metal content of this particular star. The change is relatively small, and only repeated recycling and reprocessing of the same material by subsequent generations leads to accumulation of metals in numbers significant enough to differentiate the generations.