If the group assignments are mutually exclusive (no person is assigned to more than one group ... which doesn't look to be the case, as 'apatnayi' is in groups 2 and 4), rather than loop through each of the groups, it's easier to have the lookup be a mapping of the group assignments:

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' }++;
}
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If it's not, then you can have the lookup be to an array of what groups they're in, so you don't have to look through each group every time:

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