At least, it was completely my own fault, but seems that some unobvious details must be explained.
Cause of trouble was in the Exim misconfiguration. When I've try to set
$rcmail_config['smtp_server'] = '';
to anything instead empty '' - to 'localhost' or 'my.domain.com' - RC was rejected by Exim. Changing ACL rules order was enough to fix that.
If you don't want to fall in trouble like me, keep in mind that settings
$rcmail_config['smtp_server'] = 'localhost';
$rcmail_config['smtp_port'] = 25;
$rcmail_config['smtp_user'] = '%u';
$rcmail_config['smtp_pass'] = '%p';
are functional ONLY when 'smtp_server' in non-empty and normal smtp-session occurs.
Yes, you can still use non-smtp connection between RC and MTA but remember, that "envelope-from" and "Return-Path" in headers become
www@your.domain.com, where "www" - is the account your http-server have use. That means, that all bounces and delivery service messages will be sent by outer MTAs to www@ instead original sender.
Have a nice day.