Hi,
To me it’s clearly inadvertent, especially if your initial correspondence went to a completely different person. Moreover, when it came to light that the Chair was your external examiner, you took the appropriate action(s). As long as you have a record of this, i.e., the email chain, I believe you should be fine. I would probably run it past your supervisor/advisor of studies though just so he/she is not caught off gaurd if this gets brought up at a later date.
Good luck.