Hello Jeremy,
Hmmm... This is not possible at the moment through the web interface but could be a good feature request to be able to listen to CustomField changes as an event.
Some Ideas:
Maybe you could transfer tickets through the web service based on your needs as a workaround?
Or
Add a comment through the web service after you add the custom fields and catch that event instead?
I am going to change the type of this thread so that others can vote it up.
Hope this helps!