Exchange 2013 external internet access Outlook 2013 prompts for password

Hello, we have two servers (1 Client access and 1 Database) of Exchange 2010 and four servers with NLB and DAG (2 Client access and 2 Database) of Exchange 2013. When domain joined computers are connected to the external network opening Outlook 2013 prompts for credentials. I think it should use computer authentication to open Outlook. My mailbox is in Exchange 2013 server, but we still have some users in 2010 Exchange so we can't decomission 2010 servers yet. Here are our configuration:

Get-OutlookAnywhere:

Exchange 2010 CAS

ServerName                         : EXCH1
SSLOffloading                      : False
ExternalHostname                   : ***.lt
InternalHostname                   :
ExternalClientAuthenticationMethod : Ntlm
InternalClientAuthenticationMethod : Ntlm
IISAuthenticationMethods           : {Ntlm}
XropUrl                            :
ExternalClientsRequireSsl          : True
InternalClientsRequireSsl          : False

Exchange 2013 CAS:

ServerName                         : EXCH131
SSLOffloading                      : True
ExternalHostname                   : ***.lt
InternalHostname                   : ***.lt
ExternalClientAuthenticationMethod : Ntlm
InternalClientAuthenticationMethod : Ntlm
IISAuthenticationMethods           : {Basic, Ntlm, Negotiate}
XropUrl                            :
ExternalClientsRequireSsl          : True
InternalClientsRequireSsl          : True

Other Exchange 2013 CAS:

ServerName                         : EXCH132
SSLOffloading                      : True
ExternalHostname                   : ***.lt
InternalHostname                   : ***.lt
ExternalClientAuthenticationMethod : Ntlm
InternalClientAuthenticationMethod : Ntlm
IISAuthenticationMethods           : {Basic, Ntlm, Negotiate}
XropUrl                            :
ExternalClientsRequireSsl          : True
InternalClientsRequireSsl          : True

Can the issue be of Exchange 2013 CAS configuration of IISAuthenticationMethods {Basic, Ntlm, Negotiate}? Our Autodiscover configured through SRV record in public DNS.

Sorry for my bad English, hope you understood my problem. Thanks for any help.

EDIT: I've created test Exchange 2010 mailbox and it prompts for credentials on external network too.