Direct numerical simulations, for a stratified flow in an HCCI engine-like conditions, are performed to investigate the exhaust gas recirculation (EGR) and temperature/mixture stratification effects on autoignition of synthetic dimethyl ether (DME) in the negative temperature combustion (NTC) region. Detailed chemistry for a DME/air mixture is employed and solved by a hybrid multi-time scale (HMTS) algorithm to reduce the computational cost. Three ignition stages are observed. The effect of NO to mimic the EGR effect on autoignition are studied. The results show that adding NO enhances autoignition by the rapid OH radical pool formation (one to two orders of magnitude more OH radicals results in 13%-25% reduction in ignition delay times for 1000 ppm initial NO from EGR) and increases the low temperature ignition heat release rate (QLTC) with approximately similar ignition heat release rates at the second and third ignition stages. Sensitivity analysis is performed and the important reactions pathways are specified. The DNS results show that the scales introduced by the mixture and thermal stratifications have a strong effect after the low temperature chemistry (LTC) ignition. Compared to homogenous ignition, stratified ignitions show similar first autoignition delay times, but about 19% reduction in the second and third ignition delay times. Stratification, however, reveals lower space averaged LTC ignition heat release rate and higher averaged hot ignition heat release rate compared to homogenous ignitions. The results also show that molecular transport plays an important role in stratified low temperature ignition, and that the scalar mixing time scale is strongly affected by local ignition. Two ignition-kernel propagation modes are observed: a wave-like, low-speed, deflagrative mode and a spontaneous, high-speed, kinetically driven mode. Three criteria are introduced to distinguish these modes by different characteristic time scales and Damkhöler number using a progress variable conditioned by a proper ignition kernel indicator (IKI). The spontaneous ignition mode is characterized by low scalar dissipation rate, high displacement speed flame front, and high mixing Damkhöler number. The proposed criteria are applied successfully at the different ignition stages.