The alternator is backfeeding the electrical system. Using an internal alt with alt in 3-wire configuration, the voltage sense wire should be on its own ign/acc terminal separate from the ignition contacts on the ignition switch.
As long as the sense wire has voltage supplied onto it, the alt is live. When the voltage is taken away, alt dies, engine quits.
Or somewhere along the wiring, you've wired the two circuits together. My bet is the alternator is still supplying volts.
Many 70's vehicles came with a two separate IGN terminals, one for ignition and the other for the alternator.