How do auras work?

The description of Sona's auras are quite confusing. For instance, the description of the aura of Hymn of Valor reads "Sona gains an aura for 3 seconds. Allied champions that enter the aura will gain an additional 20/30/40/50/60 (+20% Ability Power) magic damage on their next attack." What happens if they exit the aura? Do they still get the bonus damage? If so, for how long? Similar difficulties with the other auras.

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