I am facing a small problem while using Twilio conference.
My API gets incoming call and puts caller to new and empty conference room:
You could use the Twilio REST API to make an outbound call, and direct that call into your conference room. In PHP this can be done like this:
(This is from the twilio-php helper library)
require('/path/to/twilio-php/Services/Twilio.php');
$client = new Services_Twilio($sid, $token);
$call = $client->account->calls->create(
'some-twilio-number', // From a valid Twilio number
'other-number-to-call', // Number to call
'http://example.com/some_twiml'
);
The URL you use here should serve TwiML that puts the caller into the same room as your original call (exactly as you have in your question). In effect, one person called you, then you called the other person and put them into the same room.
(In the interests of full disclosure, I worked for Twilio.)