hash =
{
    a=>[];
    b=>[]
    c=>[]
   .
   .
   .
}

#some time later
my $key = "alpha"
my $array = $hash->{$key};
[download]

At this point there isn't anything at $hash->{$key}, so $array isn't pointing to anything real. When I push onto $array, that memory will get allocated happily, and won't create anything in the hash (which is a very good thing). If instead, the first thing I do is to shove something into @{$hash->{$key}}, a new entry gets magically allocated, and then everything works as expected.

Obviously I'm not one with the perl yet.

This is precisely where tlm's suggestion(++) comes in handy:
You could do:

my $array = $hash->{$key} ||=[];
[download]

This would initialize the hash value to an empty array ref, when necessary.

     "Income tax returns are the most imaginative fiction being written today." -- Herman Wouk