Question: If I build a module with a indexer, is Magento going to run the reindex automatically each night or do I need to create a cronjob for it?

Answer: 
If you want the reindex happen automatically, you need to set a cronjob for that. Please refer [here](https://magento.stackexchange.com/questions/269624/how-to-check-whether-the-reindex-working-or-not-in-magento) for detailed explanations:
Automatic re-indexing always require a active Cronjob