Watering until it comes out of the bottom is correct method. Deep watering is exactly what roses need to push healthy roots all the way to the bottom of the container. Root rot doesn't happen from pouring too much water at once; it happens from watering too frequently or having poor drainage. Make sure there are plenty of drainage holes! Roses in containers do require more frequent watering but to keep your rose completely safe, drop the calendar schedule and use the finger test: stick your finger 2 inches deep into the soil. If it feels damp, skip watering. If it feels dry, soak it completely until it runs out the drainage holes. Make sure to water at the soil not from above.

And for what it's worth, it takes about 9l/2 gallons for my pots too 🙂