Since Text::ParseWords is a core it should not be a problem to use it.

Here is my attempt:

#!/usr/bin/perl
use strict;
use warnings;
use Text::ParseWords;

while ( my $line = <DATA> )
{
    chomp $line;
    my @fields = quotewords( ',', 0, $line );
    my @lastfield;
    if ( index( $fields[-1], ',') > -1 )
    {
        @lastfield = quotewords(',',0,$fields[-1]);
        $fields[-1] = shift @lastfield;
    }
    @fields = map { '"'.$_.'"' } @fields; # if quotes are obligatory
    print join( ',', @fields ), "\n";
    while ( my $rest = shift @lastfield )
    {
        $rest = '"'.$rest.'"';
        my @temp = ('   ') x scalar @fields - 1; # three spaces, 
                                     # two of these because of quotes
        push @temp, $rest;
        print join(' ', @temp ), "\n";
    }
}

__DATA__
"A","B","C","D"
"A","B","C","D,E,F"
"A","B","C","D"
"A","B","C","D,R,T"
[download]

The output:

"A","B","C","D"
"A","B","C","D"
            "E"
            "F"
"A","B","C","D"
"A","B","C","D"
            "R"
            "T"
[download]