Strange behavior of exchange server with no user mailboxes

Hi!

Two days ago I installed the second exchange server – Exc02. Currently Exc02 has no user mailboxes at all.

Both of my Exchange servers are 2013CU9 without DAG and Shadow Resilience.

Today I have noticed that some internal emails go through my new Exchange server. 

I can’t figure out why Mailbox Transport Service on Exc01 sends email via exc02 so far as recipient‘s mailbox is on the same server (Exc01)?

Here are output from Get-MessageTrackingLog, Delivery report from ECP and a message header.

Timestamp           Source      EventId   ConnectorId                           ClientHostname      ServerHostname
---------           ------      -------   -----------                           --------------      --------------
28.10.2015 18:52:21 STOREDRIVER RECEIVE                                          Exc01  		Exc01
28.10.2015 18:52:22 SMTP        RECEIVE   Exc02\Default Exc02                	 Exc01  		Exc02
28.10.2015 18:52:22 AGENT       AGENTINFO                                        Exc02
28.10.2015 18:52:22 STOREDRIVER SUBMIT                                           Exc01                  Exc02
28.10.2015 18:52:22 STOREDRIVER DELIVER                                          Exc02 			Exc01
28.10.2015 18:52:22 SMTP        SEND      Intra-Organization SMTP Send Connector Exc02                  Exc01  	 

Delivery Report for  User2 ‎(user2@contoso.com)‎
Submitted
10/28/2015 18:52 Exc01
The message was submitted to Exc01.contoso.com.
Pending
10/28/2015 18:52 Exc02.contoso.com
Message was received by Exc02.contoso.com from Exc01.contoso.com.

10/28/2015 18:52 Exc02.contoso.com
The message has been transferred from Exc02.contoso.com to Exc01.contoso.com.
Delivered
10/28/2015 18:52 Exc01.contoso.com
The message was successfully delivered.

Received: from Exc02.contoso.com (10.117.1.19) by
 Exc01.contoso.com (10.117.1.18) with Microsoft SMTP Server (TLS) id
 15.0.1104.5 via Mailbox Transport; Wed, 28 Oct 2015 18:52:21 +0300

Received: from Exc01.contoso.com (10.117.1.18) by
 Exc02.contoso.com (10.117.1.19) with Microsoft SMTP Server (TLS) id
 15.0.1104.5; Wed, 28 Oct 2015 18:52:21 +0300

Received: from Exc01.contoso.com ([::1]) by Exc01.contoso.com
 ([::1]) with mapi id 15.00.1104.000; Wed, 28 Oct 2015 18:52:21 +0300
From: User1 <User1@contoso.com>
To: User2 <user2@contoso.com>
Date: Wed, 28 Oct 2015 18:52:21 +0300

Btw, is it possible to sort output from Get-MessageTrackingLog command in a horological order? TimeStamp is not suite because it has no milliseconds.