Experiments of autoignitive jet flames in a hot and vitiated coflow have previously shown various flame behaviors, spanning lifted flames to moderate or intense low oxygen dilution (MILD) combustion. For better understanding the behavior of flames in this configuration, regime diagrams and ignition delay results are presented from well-stirred reactor calculations across a wide range of operating conditions for methane and ethylene fuels. In conjunction with two-dimensional calculations, the importance of flame precursors and oxygen penetration across the reaction zone is revealed. It is found that widely accepted definitions and regime diagrams are inadequate to classify and reconcile the different flame behaviors that are observed experimentally. For accurate prediction of the ignition process, it is necessary to incorporate boundary conditions that capture minor species in the oxidizer. The role of fuel type also has a major impact on the ignition process and flame appearance.