My first thought was that time in my $time = time(); might not be CORE::time(). But it doesn't seem to matter.

use strict;
use warnings;

BEGIN {
  no warnings qw(redefine);
  *CORE::GLOBAL::time = sub { 4 };
}

use subs qw( time );
sub time { 5 }

my $time = time();

1;
[download]

main::(a.pl:12):        my $time = time();
  DB<1> n
main::(a.pl:14):        1;
  DB<1> x $time
0  5
  DB<2> x time()
0  5
[download]

Sorry, no idea.