New tags or new product references are not found when using the Search option on your store?
To add new products or tags to the search engine, they will need to be added to the index.
The Search engine (index) of your site being managed by PrestaShop, the manipulation is done directly in the backoffice > Preferences > Search.
Is it recommended to setup a CRON task to run a rebuild of the index automatically.
The URL to use will be displayed on the same page in your PrestaShop Backoffice.
Also note that when you modify a product, whether in PrestaShop or in Store Commander, this product is automatically re-indexed. This is the normal behavior in PrestaShop.
When you modify a product (one at a time) in PS, you need to hit the save button to validate the changes. Hitting the save button reindexes the product automatically.
However, this is slightly different in SC because the module allows you to modify multiple products in one manipulation. Saving each of these modifications on each product (imagine copy/pasting on 100 products) would drastically slow down the interface up to crashing it.
There should be a CRON task setup for the index to be rebuild as many times are needed on your store.