In a flashback scene from 2011 - i.e. shortly after Emma's first arrival in Storybrooke - Ingrid extracts some of Emma's memories with her magic. At the time, the town in present-day Maine was known as "the Land without Magic", as no magic of any kind was present in Storybrooke. So Ingrid would not have been able to use magic on Emma, even if it was her own. However, it is possible she brought some magic with her from Arendelle.