Nanoparticles (NPs) that contain both organic molecules and inorganic metal or metal oxide colloids in the same NP core are "composite nanoparticles" which are of interest in many applications, particularly in biomedicine as "theranostics" for the combined delivery of colloidal diagnostic imaging agents with therapeutic drugs. The rapid precipitation technique Flash NanoPrecipitation (FNP) enables continuous and scalable production of composite nanoparticles with hydrodynamic diameters between 40-200 nanometers (nm) that contain hydrophobic superparamagnetic iron oxide primary colloids. Composite NPs co-encapsulate these primary colloids (diameters of 6 nm, 15 nm, or 29 nm), a fluorescent dye (600 Daltons), and poly(styrene) homopolymer (1800, 50 000, or 200 000 Daltons) with NPs stabilized by a poly(styrene)-block-poly(ethylene glycol) (1600 Da-b-5000 Da) block copolymer. Nanoparticle assembly in FNP occurs by diffusion limited aggregation of the hydrophobic core components followed by adsorption of the hydrophobic block of the stabilizing polymer. The hydrodynamic diameter mismatch between the collapsed organic species and the primary colloids (0.5-5 nm versus 6-29 nm) creates a diffusion-aggregation time scale mismatch between components that can lead to nonstoichiometric co-encapsulation in the final nanoparticles; some nanoparticles are composites with primary colloids co-encapsulated alongside organics while others are devoid of the primary colloids and contain only organic species. We use a magnetic capture process to separate magnetic composite nanoparticles from organic-only nanoparticles and quantify the amount of iron oxide colloids and hydrophobic fluorescent dye (as a proxy for total hydrophobic polymer content) in the magnetic and nonmagnetic fractions of each formulation. Analysis of the microstructure in over 1100 individual nanoparticles by TEM imaging and composition measurements identifies the conditions that produce nonstoichiometric composite NP populations without co-encapsulated magnetic iron oxide colloids. Stoichiometric magnetically responsive composite NPs are produced when the ratio of characteristic diffusion-aggregation time scales between the inorganic primary colloid and the organic core component is less than 30 and all NPs in a dispersion contain organic and inorganic species in approximately the same ratio. These rules for assembly of colloids and organic components into homogeneous composite nanoparticles are broadly applicable.