You used (?!, which is a look-ahead. You needed a look-behind. Unfortunately, variable length look-behind is not implemented (and "moderate" is longer than "mild"). So, you have to reverse your string and use a negative variable length look-ahead:

#!/usr/bin/perl
use warnings;
use strict;
use feature qw(say);


my @w = ('active', 'not active', 'mild active', 'moderate active');

for (@w) {
    my $r = reverse;
    say "$_: ", $r =~ /evitca(?! dlim| etaredom)/ ? 1 : 0, '.';
}
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