I'm not an expert on inflation, but here's my understanding.
Inflation models assume some kind of GUT (perhaps a variation of SU(5)) which is spontaneously broken around 10^15 GeV, which corresponds to 10^-36 s.
If inflation occurs before GUT symmetry breaking, it does not solve the monopole problem (we should see lots of magnetic monopoles but we don't).
If inflation occurs too late after GUT symmetry breaking, we have a problem of baryogenesis. Baryogenesis requires the availability of baryon number changing interactions, we know that there aren't any in the explored region of energies, but most GUTs allow such process near GUT scale. Problem is, inflation wipes any traces of baryogenesis that occurs before its onset, just as it scatters magnetic monopoles.
Therefore the solution is to have inflation right around the GUT scale, it spreads out magnetic monopoles sufficiently to make them virtually unobservable, and then, when inflation is over, the system experiences reheating and gets close enough to the GUT scale again to generate baryons.