We must not doubt that the couple actually died at the moment Adam ingested the forbidden fruit. 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.