That would depend on how you pronounce "hysterically".
Do you voice the "h" or not?
If you pronounce it "iss-tear-ick-lee" then you'd use "an".
If you pronounce it "hiss-tear-ick-lee" then you'd use "a".
Personally I've never heard the word pronounced with a silent "h". I checked several dictionaries and they all list the word with voiced "h". None of them even list the silent "h" as an alternate pronunciation.
Therefore I would say that the voiced "h" is the correct pronunciation, and "an hysterically funny person" is wrong.
Given the "did you see" comment, it's a good example of a hypercorrection:
