So, I've confirmed that currently the API does not offer methods to notify you of changes. However, if you're willing to find workarounds or else make some local code changes, then it may be possible to get at least some of your needs met regardless. Some pieces that might help:
AtoM does have a basic audit log functionality for archival descriptions. This is tracked and stored in the database, using the date-time stamps. See:
There's also the description updates module, which allows administrators to search for records based on date ranges of creation or modification. When the description change log has been enabled, it also includes a User filter. See:
When the audit log is not enabled, this functionality uses the Elasticsearch index to provide results - AtoM uses ES version 5.6 in the 2.6 release. Elasticsearch also includes its own API that might help you get the information you need. Consult the ES 5.6 documentation
for more information.
The API itself supports most parameters available for searching in the user interface, including sorting by last modification date. Right now the response does not include actual date or time stamps, but it could likely be modified to include this.
Hopefully at least some of these pieces might help you create a strategy to get the information you need.