How do we use the drying rack, storage and steam steriliser?

New father here! My confinement nanny steam sterilised the bottles, then place on the bottle drying rack to dry before putting into a container to cover and keep. Is that the correct way to use all these things? I was thinking after sterilised if we put outside to dry, won’t it defeat the sterilisation? I would love to use direct from the sterliser but there’s limited space it can hold. Anyone share how you do it? And the storage container need to be in the fridge?