Ok. After some tests, I get what you are saying.

The /g flag does not require that further matching must start past the end of the previous match--it just makes a request for any other unique matches. And the regex /(\w\w\w)*?TGA/ can act like the regex /TGA/ because a regex will happily match nothing for *.

But then why doesn't the /g flag cause this to match four times:

use strict;
use warnings;
use 5.010;

my $str = 'aaaBBBcccTGA';
while ($str =~ /(?:\w\w\w)*?(TGA)/g) {
    say $1;
    say pos $str;
}
[download]

Aren't there four unique matches:

1)  when (\w\w\w) is matched 0 times.
2)  when (\w\w\w) is matched 1 time.
3)  when (\w\w\w) is matched 2 times.
4)  when (\w\w\w) is matched 3 times.

That suggests that another match must end past the previous match--but that the next match doesn't have to start past the previous match.

My tests also show that starting the regex with a \A to anchor it to the beginning of the string will cause the regex to match only once:

use strict;
use warnings;
use 5.010;

my $str = 'aaaBBBcccTGAddTGA';
while ($str =~ /\A(?:\w\w\w)*?(TGA)/g) {
    say $1;
    say pos $str;
}

--output:--
TGA
12
[download]

But then I would expect this to match twice, and it doesn't:

use strict;
use warnings;
use 5.010;

my $str = 'aaaBBBcccTGAdddTGA';
while ($str =~ /\A(?:\w\w\w)*?(TGA)/g) {
    say $1;
    say pos $str;
}
[download]

So I guess I don't have any idea what's going on.

The /g flag does not require that further matching must start past the end of the previous match--it just makes a request for any other unique matches.

No. It makes a request for another match to the leftright of the end of the previous match. The first match goes up to position 12:

aaaBBBcccTGAddTGA
XXXXXXXXX
         TGA
           ^ match ends here
[download]

So the next match sees only <c>ddTGA</cc> to match against.
Perl 6 - links to (nearly) everything that is Perl 6.

Do you mean to the 'right' of the end of the previous match?