In addition to dripping water, I'd measure the SG along the way and discard some water from the container from time to time. The goal is to raise the SG perhaps 0.001 units every 15-30 minutes, depending on the animal in question, until the SG is close to that of the tank.
Most instructions just say to drip until the volume of water is doubled or tripled, and that's not good enough, in my opinion. Doubling the volume of water will move the SG halfway between the tank and the container, which could leave quite a salinity shock.