I don't think that there is a DNS or reverse DNS problem.
here are test results from
MX Lookup Tool - Check your DNS MX Records online - MxToolbox on both domains and you see there is a problem on domain-b.com
220 domain-a.com ESMTP Postfix
Not an open relay.
0 seconds - Good on Connection time
0.671 seconds - Good on Transaction time
OK - 81.xxx.xxx.xxx resolves to domain-a.com
OK - Reverse DNS matches SMTP Banner
220 domain-b.com ESMTP Postfix
Not an open relay.
0 seconds - Good on Connection time
0.624 seconds - Good on Transaction time
OK - 81.xxx.xxx.xxx resolves to domain-a.com
Warning - Reverse DNS does not match SMTP Banner
Thanks,
-Aki