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my %lookup = map {
  my $grp = $_;
  map { $_ => $grp } ( @{ $groups{$grp} };
...
    # ... or, to track those users with no groups
    # $output{$time}{ $lookup{$name} || 'unknown' }++;
}

my %lookup = ();
foreach my $grp (keys %groups) {
    push @{$lookup{$_}}, $grp foreach @{$groups{$grp}};
...
foreach my $name (@usernames) {
    $output($time){$_}++ foreach @{$lookup{$name}};
}