The answer to your specific question as to why your code doesn't export the version to My::Package::A is that, as you already noted, caller(2) is main for some reason. However, if you do a full call stack trace from the import, you will see that My::Package::A is included but there are two instances of main in between it. I don't really have any idea why that is (perhaps a more enlightened monk can explain) but this causes the condition of your while loop to fail and thus not go futher into the call stack.

I believe what you want, and probably intended to do, is to simply skip packages not begining with My::Package but continue the loop. Like so:

./My/Package/Version.pm:

package My::Package::Version;

use strict;
use vars qw(@ISA @EXPORT $VERSION);

use Exporter;
@ISA = qw(Exporter);
@EXPORT = qw($VERSION);
$VERSION = 3.14;

sub import {
  my $i = 0;
  my $pkg = caller(0);
  print "Import Caller Trace:\n";
  while($pkg) {
    print "  Called from package $pkg\n";

    # Note that these tests have been moved from the
    # loop condition to inside the loop so the loop
    # will not terminate if it fails.
    if($pkg =~ /^My::Package::/ and not defined ${"$pkg\::VERSION"}) {
      print "    (Exporting VERSION to $pkg)\n";
      __PACKAGE__->export_to_level($i+1);
    }
    $pkg = caller(++$i);
  }
}
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./My/Package/B.pm:

package My::Package::B;

use My::Package::Version;

print "My::Package::B loaded.\n";

1;
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./My/Package/A.pm:

package My::Package::A;

use My::Package::B;
@ISA = ('My::Package::B');

print "My::Package::A loaded.\n";

1;
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./tst.pl:

#!/usr/bin/perl

use lib '.';
use My::Package::A;

print "\$My::Package::A::VERSION = $My::Package::A::VERSION\n";
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Output of ./tst.pl:

Import Caller Trace:
  Called from package My::Package::B
    (Exporting VERSION to My::Package::B)
  Called from package main
  Called from package main
  Called from package My::Package::A
    (Exporting VERSION to My::Package::A)
  Called from package main
  Called from package main
  Called from package main
  Called from package main
  Called from package main
My::Package::B loaded.
My::Package::A loaded.
$My::Package::A::VERSION = 3.14
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bbfu
Black flowers blossum
Fearless on my breath