Because translations are automatically saved in POEditor, our service does not offer an option to trigger an export each time someone adds a translation to a language in a localization project (this could easily get spammy).
However, as a workaround, you can make an API script to check for updated translations and trigger an export only when updates are found.
Keeping the date of the last export and comparing it with the date a language was last updated in the project, you can find out if any new translations were added to that language. You can use the languages/list method to see when a language was last updated.
If you'd rather automate the export of fully translated languages only, or of fully translated and proofread languages, you can set a Language Completed or Language Proofread callback on the project. These callbacks will tell your script what language was completed or completed and proofread, so that the script can trigger an export.
If you are using an integration with a code hosting platform such as GitHub, Bitbucket, GitLab or Azure DevOps, you can also include webhooks to the workflow to automate the export to your repo(s). Just create an export webhooks for each language and add them to your script, so that the script knows to trigger the appropriate webhook when it receives a signal from the callback.