A good command for testing if your TLS setup works in exim4 is:
swaks -s insert.host.name.here -tls -q ehlo
It goes something like this.
~$ swaks -s insert.host.name.here -tls -q ehlo
=== Trying insert.host.name.here:25…
=== Connected to insert.host.name.here.
EHLO debian
<- 250-insert.host.name.here Hello somewhere.com [81.107.112.224]
<- 250-SIZE 52428800
<- 250-PIPELINING
<- 250-AUTH PLAIN_TEXT LOGIN
<- 250-STARTTLS
STARTTLS
EHLO debian
<~ 250-insert.host.name.here Hello cpc2-cable.ntl.com [8.0.1.4]
<~ 250-SIZE 52428800
<~ 250-PIPELINING
<~ 250-AUTH PLAIN_TEXT LOGIN
QUIT
<~ 221 insert.host.name.here closing connection