As far I know, 普通に mean normally/ordinary in English. So I've seen it use a lot of times like this.
However, there are a lot of contexts which it seems like the speaker uses it to show surprise
One example I met recently
今日久しぶりに女とキスしたんだけど、普通に嫌だったんだよな
The character used to be a playboy but after settling into a relationship, he stopped seeing many girls. However, recently one of his exes kissed him and he confesses this to his current partner. The 普通に here seem to be used similar to 意外に?
How are Jisho 2 and 3 definition used?
The definition
- normally; ordinarily; usually; generally; commonlyOnly applies to ふつうに, See also 普通 Adverb (fukushi)
- by anyone's standards; by normal standards; sufficiently; actually; genuinely; trulyColloquial, used when giving a positive assessment, esp. of something that exceeds expectations Adverb (fukushi)
- without any issues; without any difficulty; (surprisingly) well; just fine; naturallyColloquial, describes an