question about fuel pump

Hey I was wondering if anyone know for sure if the fuel pump is supposed to turn on as soon as the key is set to the ON position on a 91 or around that Talon/eclipse or laser. Mine only turns on when onthe start position and i think this is causing my car to die after started

On DSMs the pump only runs while there is a signal from the cam angle sensor, so it will come on as soon as you start to crank the motor over. ITs builds pressure instantly, so this is not likely the cause of your problem.