This work investigates an auto-igniting impulsively started jet flame issuing into hot and vitiated co-flow by Large Eddy Simulation (LES) with multidimensional detailed tabulated chemistry. The experiment from DLR (German Aerospace Center, Stuttgart) is reproduced. The combustion model includes the scalar dissipation rate effects and pressure dependency, where the pressure is used to couple the tabulated chemistry to the compressible solver. We identify the effect of (weak) pressure perturbations and analyze auto-ignition (AI) properties in pulsed flames and their variations on different realizations. For the former task, two separate simulations are performed in density- and pressure-based formulations with the same boundary conditions. A good agreement was achieved between both of the solvers and the experiments for the statistically steady jet, providing evidence that the combustion model is suitable for the pulsed jet. Both solvers managed to describe the mixing dynamics well. However, they slightly underpredicted the lift-off height of the flame, where we suspect a minor overestimation of the flame propagation speeds. The transient jet was simulated for 20 pulse cycles to achieve pulse statistics of AI. The estimated delay times and the location of the AI matched experimental observations. The AI kernels always emerged on the lean-side of the mixing layer at the so-called most-reactive mixture fraction, and at various heights above the burner for each pulse cycle. It was observed that AI was extremely sensitive to the local temperature field, where a slight temperature variation caused a significant change in AI delay time and location. Finally, the statistics showed slight variations between the pulses for the most-reactive mixture fraction, likely caused by turbulent fluctuations of the flow field. Overall, the results show that the tabulated chemistry model is able to reproduce the AI delay time and location with a satisfactory agreement.