Setting of POP is the result of:
SETTING REACTIONS
The most widely accepted mechanism is the dissolution-precipitation theory, which is based on dissolution of the hemihydrate particles in water followed by instant recrystallization to the dihydrate. This reaction has become possible because the solubility of hemihydrate in water is four times greater than that of the dihydrate near room temperature. Thus, the setting reactions occur as follows:

When the hemihydrate is mixed with water, a suspension is formed that is fluid and workable.
The hemihydrate dissolves until it forms a saturated solution of Ca2+  and (SO4)2−.
This saturated hemihydrate solution is supersaturated with respect to the solubility of the dihydrate; precipitation of dihydrate occurs.

Key Concept:
Setting reaction has become possible because the solubility of hemihydrate in water is four times greater than that of the dihydrate near room temperature.
Reference: PHILLIPS’ SCIENCE OF DENTAL MATERIALS, 12th ed page no 183
Difference in solubility of CaSO4.1/2 H2O + CaSO4. 2H2O
Reaction between CaSO4. 2H2O and water
Nucleation and growth of CaSO4.1/2 H2O crystals
Reaction between hemihydrate and dihydrate