The occurrence of concentration and temperature gradients in saline microdroplets evaporating directly in air makes them unsuitable for nucleation studies where homogeneous composition is required. This can be addressed by immersing the droplet in oil under regulated humidity and reducing the volume to the picoliter range. However, the evaporation dynamics of such a system is not well understood. In this work, we present evaporation models applicable for arrays of sessile microdroplets with dissolved solute submerged in a thin layer of oil. Our model accounts for the variable diffusion distance due to the presence of the oil film separating the droplet and air, the diffusive interaction of neighboring droplets, as well as the variation of the solution density and water activity due to the evolving solute concentration. Our model shows excellent agreement with experimental data for both pure water and NaCl solution. With this model, we demonstrate that assuming a constant evaporation rate and neglecting the diffusive interactions can lead to severe inaccuracies in the measurement of droplet concentration particularly during nucleation experiments. Given the significance of droplet evaporation in a wide array of scientific and industrial applications, the models and insights presented herein would be of great value to many fields of interest.