The essential part is this: 
>>> STARTTLS Net::SMTP=GLOB(0x83f812c)
<<< 220 2.0.0 continue Net::SMTP::_SSL=GLOB(0x83f812c)
>>> EHLO oh01lx03.workflowone.net Net::SMTP::_SSL=GLOB(0x83f812c)

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This means you successfully send the STARTTLS command, got a successful response and issued a new EHLO inside the TLS upgraded connection. If you want to be really sure you could also ask for the cipher used within the connection, e.g.: 
my $smtp = Net::SMTP->new(...);
$smtp->starttls or die;
print "encrypting with cipher=".$smtp->get_cipher."\n";

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In reply to Re: NET::SMTP with TLS by noxxi
in thread NET::SMTP with TLS by bdegan2

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