It may be all in equilibrium (while calcium phosphate is weakly soluble it is still soluble, there are other precipitates like CaHPO4, plus some calcium/phosphate complexes) and kinetics (complexation, hydrolysis and precipitation). Thus you may have some some low but constant concentration of calcium for some time - long enough to catalyze crosslinking. But that's just guess.
You may try to check how fast pH changes, as that will give some insight into preicpitation kinetics.