A flame out the back is not necessarily a result of a hot start. It often is due to residual fuel in the MO2 after a shutdown or prolonged running of the booster pump after maintenance intervention or during ops with a fuel pump seal that is getting old thus allowing the fuel past instead of back to the tank etc and is often just residual fuel causing a secondary ignition not affecting the T4 reading due to it occuring after the probes. Not saying it is the case but have seen it many a time. On the Arriel 2 at night during a start shortly after shutdown you will be shocked to see the size of the flame when you hear the explosion sound on start-Arriel 2 no min T4 before start on AS350. Have seen a few 120's do this without T4 exceedance. The VEMD receives the T4 signal as it is displayed and it will be recorded as a over limit if it exceeded regardless of the N1. A flight is constituted from 60% N1(defaults to FLI) to 50% N1 on shutdown(defaults to 3 arc screen) and gets displayed below 10% N1 on the lower screen as the flight report. The n1 and 2 cycles is the percentage used from 0-max-0 and is the reason for it often being a decimal and not a full cycle as you do not reach max N1/2 every flt.
No expert but hopes this help. Will double chk in any case the facts and figures so do not quote me yet. Ask your engineer to print you chap 31 out of the description and operational manual and all your questions will be answered.