Hi,
That sounds very strange. The cron process runs periodically, but it won’t index everything all at once to save resources. If you add for example over 100 items at once, it may take a few executions to index.
You can trigger the deletion of the index table, but then it has to be indexed again, but then again it takes multiple requests to index everything via CRON depedning on the database size. You will have basically an empty index maybe for a couple of hours or even more.
I would rather recommend executing the save_post action hook after each and every item when it is imported. That will automatically trigger everything that is attached to that hook, including the indexing. It might be much easier to add this to the API endpoint, as this should be already executed by default.