We performed the first optical tweezers experiment on droplets to which secondary organic matter (SOM) was added through in situ precursor ozonolysis directly in the tweezing chamber. The alpha-pinene SOM formed a composite droplet with separate phases when added to an aqueous salt or a squalane droplet, producing a shell of secondary organic matter. Using spreading coefficients, we can bound the surface tension of alpha-pinene SOM and conclude that the air-liquid surface tension of alpha-pinene SOM is less than or equal to that of squalane, 28 mN/m. This, in turn, helps to constrain the Kelvin diameter for condensation of alpha-pinene SOM onto ultrafine particles soon after nucleation in the atmosphere. Analysis of the WGMs in the Raman spectrum allows us to conclude that the nucleated submicron SOM particles that coagulated with the trapped droplet must quickly spread across the droplet under a timescale much shorter than the Raman spectrum acquisition time of 2 seconds, otherwise the WGMs would not have been present. On aqueous cores we observed that the coating of SOM does not impede water equilibration timescales.