Usually that will work. Sometimes a colony will be stubborn and won't move. That's when you have to use other techniques. This is what I have done and all have worked.
Heat the new test-tube - They will more then likely move the brood to the heat source.
Shined a light on the old test-tube
Used an ice pack and put it on the older test-tube - Had a Camponotus Modoc colony with 100+ workers and they did not want to move out of the overcrowded/moldy smaller formarcium so i used an ice pack and put it on the older formicarium and the began to move to the newer much larger one.
Drop them in - Sometimes they will never move and when conditions are threatening there survival you have to.