There is no way to subscribe to exports made by the built-in export dialog being finished.
I can only think of one workaround method. If you read the audit log you can see if an export has been made. This might be a bit complicated and not the information will not come in in a very real-time manner, there is delays on the system writing this kind of logs. - https://developer.milestonesys.com/s/article/read-Audit-System-or-Rule-logs-from-the-MIP-SDK