In the first sense, it is a side-effect or by-product, that is, there is a causal relationship between the secondary phenomenon and the first.
In the second sense, the medical meaning, there is no such relationship. A doctor might ask a patient whom he is treating for a disease ," Have you noticed any new epiphenomena?"
(Well, mine do!!!)
Source: The American Heritage Dictionary of the English Language. 3rd ed.