If the solvent decreases in temperature during a reaction, it's because heat is lost from the solvent when reaction products are formed from the reactants. I.e., heat energy from the solvent (surroundings) is used to form the reaction products.
The solution in this case is your surroundings. The "system" is your reaction. The system is gaining energy because the products have higher energy than the reactants. Because energy is conserved, if the reaction system gains energy, the surroundings lose energy, which means the solvent decreases in temperature. Conversely, in an exothermic reaction, the products are lower energy than the reactants, so the reaction system loses energy, the surroundings gain energy, which means the surroundings (solvent) rise in temperature.