Although they did not immediately 'drop over dead', death nevertheless commenced its tyranny. Death is experienced essentially as a separation. We should think of death as separation rather than annihilation. Death is the severance of the living unions which God created. Creation is a living tapestry, a fabric of complementary components each knit together in mutual dependence having supportive functions.
Death rips that living fabric asunder.
In the couple's disobedience reality began to crack open. Divisions in the created order emerged. What God had joined together began to rip apart. But Satan's opening of our eyes is the death God threatened upon disobedience to His law. Adam now sees as a dead man, separated from God and His Word.