The flame initiation process in dual-fuel spray assisted combustion is presently not fully understood. Here, diesel spray assisted combustion of premixed methane/oxidizer/EGR is explored in the post-ignition phase by scale-resolved simulations. The modified dual-fuel ECN Spray A forms the baseline configuration. An extensive local grid refinement (approaching DNS limit) around one of the first high-temperature ignition kernels is carried out in order to examine the validity of hypothesized flame initiation and deflagration. A high quality LES is used to solve the spray dynamics, while the embedded quasi-DNS (eq-DNS) region offers detailed information on the ignition kernel evolution. The finite-rate chemistry is directly integrated, utilizing 54 species and 269 reactions. Local combustion modes are investigated for the ignition kernel development toward spontaneous ignition and premixed flame propagation using various approaches, including the reaction front displacement speed, energy transport budget, and chemical explosive mode analysis. Furthermore, a new criterion based on reaction flux analysis is introduced, which is compatible with dual-fuel combustion. The spatial and temporal scales associated with the ambient methane consumption and consequent flame initiation are characterized. For the first time in dual-fuel spray assisted simulations, numerical evidence is provided on the initiation of premixed flames, and the corresponding timescale is reported. Particularly, there is a transient mixed-mode combustion phase of approximately 0.2 ms after the spray second stage ignition wherein extinction, ignition fronts, and quasi-deflagrative structures co-exist. After such a transient period, the combustion mode becomes essentially deflagrative. Finally, interactions between turbulence and premixed flame front are characterized mostly in the corrugated regime.