[exim] exim4 tls relay to office 365, how to be sure my key…

I'm trying to configure exim4 to relay outgoing mail through office365
smarthost.
Apparently o365 requires a valid certificate with a known domain in the CN
field, otherwise the amount of mails you can send is limited and you risk
being flagged as spam or have mails refused.

I placed the cert+key i want to use in /etc/exim4/ (exim.key and exim.crt).
Everything seems to be working, but i'm not sure they are actually being
used by exim .. how can I make sure they do ?

If I rename the files and restart exim, mails are still being sent
successfully.. so that makes me wonder if my cert and key are used or not..

If i use exim's sendmail command manually, i see this in the output :

TLS: no client certificate specified; okay

If I use strace, i don't even see the process looking at
/etc/exim4/exim.key and exim.crt so i'm thinking maybe exim doesn't use
them ?

If anyone can help me i'd appreciate.
Thanks

Renaud