There is no solvated molecule of either of 4 ionic compounds. All interactions ( or lack of ) happen on hydrated ionic level, including eventual precipitation or formation of ionic pairs.
All four salts are soluble, including magnesium chromate with the solubility $\pu{137 g/100 mL}$ at $\pu{20^{\circ}C}$ (solubility table).
When dissolved, salts form independent hydrated ions:
$\ce{Mg(NO3)2(s) + Na2CrO4(s) ->[H2O] Mg^2+(aq) + 2 NO3-(aq) + 2 Na+(aq) +CrO4^2-(aq)}$
If the solution is being evaporated, the salt with lowest solubility starts precipitating the first, with the repective ions recombining into the solid, stripping off their hydration cover.
The same solution is formed, if we start with equivalent amounts of the other two salts:
$\ce{2 NaNO3(s) + MgCrO4(s) ->[H2O] Mg^2+(aq) + 2 NO3-(aq) + 2 Na+(aq) +CrO4^2-(aq)}$
Ions have no memory which ions they were paired with in the solid state.