Romans 5:15 tells us that many died because of Adam's trespass. They didn't just die physically. They experienced death (i.e., sickness, disease, lack of any kind, etc.) because of his trespass. The word trespass in Greek is paraptoma. It's two words, para, meaning close beside or an intimate connection, and pipto, meaning to fall away or abandon. -- Adam's trespass was falling away from or leaving his intimate relationship with his Father.
Do not read that with the mindset of separated from God! Adam fell away. Adam was the one who abandoned his intimate connection with His father. He separated himself from the Father. Mankind (born before the cross) through Adam had moved away from what defined them - their identity in God. When Adam abandoned the intimate connection he had with His Father, his legacy to all mankind (from himself to the cross) was death reigning. Because of Adam's transgression, death grabbed the opportunity to dominate mankind.