First off, go under Settings - then Battery - Auto launch management - ... And try to enable the noRoot app both under App auto launch and App secondary launch.
But yes Android needs to broadcast a boot complete for interested apps (listening) to start. And it is possible that your system is not properly broadcasting this (and yes this may be owing to the modifications done on the system file. Do retry flashing the stock file if possible and then retry the noroot and see if that helps. Unfortunately, this could also be a shortcoming bon the app's side, for which the developer would need to get involved.