Your console app should have one config file with this entry:
<connectionStrings>
<add name="FilingDBContainer" connectionString="Data Source=TESTPC\SQLEXPRESS;Initial Catalog=Test;Integrated Security=True;Pooling=False" />
<add name="ResponderDBContainer" connectionString="Data Source=TESTPC\SQLEXPRESS;Initial Catalog=Test;Integrated Security=True;Pooling=False" />
</connectionStrings>
Connection strings are loaded from the config of the loading application. If you want to automatically load config files for assemblies, you'll have to write code to manually query it.