As I understand it, the OP wants the hash entry to be an alias to the legacy $alpha_state variable, so that both see the same value ("I want the hash value $hash{alpha}{state} to always equal $alpha_state."). Or put differently, if either one of them is being changed, the other one automatically holds the changed value as well.
eval only assigns the value the variable holds at the time of the eval. If it changes afterwards, the hash entry will not be updated; nor will changing the hash entry update $alpha_state.