Genuinely means truly and sincerely, not just for show. The reaction that was not performed.
The word exists to head off doubt, which is why it so often sits before adjectives of feeling: genuinely sorry, genuinely surprised, genuinely pleased for you. Saying it admits that the opposite was possible. It also works as a plain intensifier meaning really, as in genuinely difficult. The adjective genuine covers both people and objects, and a genuine painting is one that is what it claims to be rather than a forgery.
Proto-Indo-European
*ǵenh₁-
Latin
genuīnus
English
genuine
English, today
genuinely
From genuine + -ly. genuine Borrowed from Latin genuīnus. From Latin genuīnus (“innate, native, natural”).
Etymology from Wiktionary, CC BY-SA