Two small tweaks (for the OP, really).

• for (...) {
     push @a, $_;
  }
  [download]

  is a long way of doing

  push @a, ...;
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  Depending on the context, it might make more sense to do just

  my @a = ...;
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• unless ( ($localtimenoformat - $mdtmnoformat) > 3600 ) {
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  can more clearly be written as

  if ( ($localtimenoformat - $mdtmnoformat) <= 3600 ) {
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• $localtimenoformat=time; doesn't need to be executed multiple times.

• What you call "no format" time could really be called "epoch" time.

     push @files, $ftp->ls;

     my $new_file = 0;
     my $current_time_epoch = time;
     for my $file (@files) {
        my $modified_time_epoch = $ftp->mdtm($file);
        if ( ($current_time_epoch - $modified_time_epoch) <= 3600 ) {
           print "$file\n";
           print "Current time =  $current_time_epoch\n";
           print "MDTM         =  $modified_time_epoch\n";
           $new_file = 1;
        }
     }

     envia_mail() if !$new_file;
     $ftp->quit or die $ftp->message;
[download]

If those print statements are just for debugging purposes, you can exit the loop early.

     push @files, $ftp->ls;

     my $new_file = 0;
     my $current_time_epoch = time;
     for my $file (@files) {
        if ( ($current_time_epoch - $ftp->mdtm($file) ) <= 3600 ) {
           $new_file = 1;
           last;
        }
     }

     envia_mail() if !$new_file;
     $ftp->quit or die $ftp->message;
[download]