As phil spells out correctly already many systems will auto append the domain they are in, be it you set it up on the system or they got it from the dhcp server, etc.
If home.de is a valid domain on the public net, it normally is not a good idea to use that as your domain on your local network - unless in fact you own said domain.
I would suggest you change your local systems to use say home.lan or home.de.lan or .local or de.home etc.. something where the .tld is not a valid on the public. This should remove any issue of it resolving to a public IP.
You can then resolve these hosts via pfsense dns or as stated create a forwarder in pfsense to send to your local dns that can resolve such domains, etc.