If you expect interleaved output, you will need to disable output buffering and make your code much slower:

sub alpha
{
        foreach my $i (900 .. 1900)
        {
                print 'A',"\t";
                sleep rand(2);
        }
}

sub numeric
{
        foreach my $j (1 .. 1000)
        {
                print $j,"\t";
                sleep rand(2);
        }
}

# Make print() output unbuffered;
$| = 1;

LINKS:
foreach my $linkarray (@links)
{
        $pm->start and next LINKS; # do the fork
...
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