If liquid fuel and oxdizer is injected in a rocket combustion chamber, the mixture will be moving relatively slow before reaching the nozzle, preventing the flame front from escaping outside the engine.
But if the fuel and oxidizer come from gas generators, they should be injected at high speeds since they are lighter, so they should be at a temperature higher than the self-ignition point, have some kind of catalyst or a very high flame front speed to keep the flame inside.
How does the combustion chamber in a full-flow staged combustion engine manage to keep the combustion inside it?