my %lookup = map {
  my $grp = $_;
  map { $_ => $grp } ( @{ $groups{$grp} };
} (keys %groups);

# ... and then below ...

foreach my $name (@usernames) {
    $output{$time}{ $lookup{$name} }++;
    # ... or, if you have users logged in that aren't in a group
    # $output{$time}{ $lookup{$name} }++ if exists  $lookup{$name};
    # ... or, to track those users with no groups
    # $output{$time}{ $lookup{$name} || 'unknown' }++;
}

##</code><code>##

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