Theoretical research into the heat and mass transfer, hydrodynamic and physicochemical processes in combustion chambers of gas turbine engines usually implies that multi-component jet fuels are modeled using single-component liquids (saturated or cyclic hydrocarbons) and their substitutes. Due to an insoluble dispersed phase (e.g., water) in their composition, droplets consist of a noncombustible core and a liquid fuel shell. During heating, water droplets coalesce in fuel droplets to produce explosion-triggering volumes of liquid superheated to the boiling point. When heated, these heterogeneous droplets breakup in the micro-explosion and puffing modes. This study reports the numerical simulation results providing the temporal characteristics of heating and evaporation of heterogeneous droplets until puffing/micro-explosive breakup, when varying the composition of the fuel shell in the homologous series of saturated and cyclic (as illustrated by monocycloparaffins) hydrocarbons from C7 to C16. The conducted research has revealed that the variations in the breakup delay times in the homologous series of saturated and cyclic hydrocarbons are nonlinear. The breakup delay rates were found to increase substantially in the boundary points of the investigated series. Mechanisms to control droplet fragmentation delay time were identified for different initial and boundary conditions. A dimensionless complex reflecting the correlation between the critical conditions of composite liquid droplet breakup and the physicochemical properties of the fuel shell components was proposed.