Split string on first occurrence of each character
Jelly, 4 bytes

QƤĠị


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Explanation

QƤĠị  Input is a string, say s = "adam"
 Ƥ    For each prefix of s: ["a","ad","ada","adam"]
Q     remove duplicates: ["a","ad","ad","adm"]
  Ġ   Group indices by equal values: [[1],[2,3],[4]]
   ị  Index into s: ["a","da","m"]


The internal representation of the strings, which the TIO link displays, is slightly different.