In what step in asthma management would a home nebulizer be used?

Both.... ..Maintenance meds (such as budesonide) and rescue meds (such as albuterol) are available in nebulizer ampoules, and can be used by people unable to use handheld mdi's (multidose inhalers).
Any. Nebulizers, in most instances, have been shown to be no more effective than metered dose inhalers (mdis), when the mdi is used properly (used with a spacer or facemask for a kiddo for maximum effectiveness). Experiences show us, however, for young children in shortness of breath, it is much easier to deliver acute relief medicine, e.g. Albuterol, via nebulizer.
At any level. Some people aren't controlled enough with their inhalers, and the nebulizer helps to bring them under control with higher levels of medications. Others do well for the most part, but can have severe wheezing with, for example, animal exposure or viral infections. In these cases, having a nebulizer at home can help prevent a trip to the emergency department.
Nebuluzer... A home nebuluzer is useful when an asthmatic cannot coordinate enough to effectively use an inhaler, even with a spacer. Most people can be taught to use an inhaler with spacer effectively. Example of when this might not be possible is young children. Ask your doctor if this therapy is right for you, your children, etc.