Not REGEX approach, but with two hashes.

#!/usr/bin/perl -l

use warnings;
use strict;

my $template = 'neocene';
my $uniq = 4;
my $len = length $template;

my @dict;
@dict = <>; # <-- 354984si.ngl
chomp @dict;

my @good = grep {
    my %occ1;
    while( $template =~ m/./g ){
        my $key = $& . substr $_, $-[0], 1;
        $occ1{ $key } ++;
        }
    my %occ2;
    map $occ2{ $_ } ++, map { ( split '' )[ 1 ] } keys %occ1;
    $uniq == keys %occ1 and
    $uniq == keys %occ2;
    } 
    grep $len == length, 
    @dict;

print for @good;
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OUTPUT:

kaitaka
lauhala
metreme
neocene
tempete
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UPD.removed mistakenly added word from the output which is absent in the dictionary.