The charging dynamics of helium droplets driven by embedded xenon cluster ignition in strong laser fields is studied by comparing the abundances of helium and highly charged Xe ions to the electron signal. Femtosecond pump-probe experiments show that near the optimal delay for highly charged xenon the electron yield increases, especially at low energies. The electron signature can be traced back to the ionization of the helium environment by Xe seed electrons. Accompanying molecular dynamics simulations suggest a two-step ionization scenario in the Xe-He core-shell system. In contrast to xenon, the experimental signal of the helium ions, as well as low-energy electron emission show a deviating delay dependence, indicating differences in the temporal and spacial development of the charge state distribution of Xe core and He surrounding. From the pump-probe dependence of the electron emission, effective temperatures can be extracted, indicating the nanoplasma decay.