When updating the price of a product in Magento, the changes should be reflected in the checkout and cart pages automatically without the need for a full reindex. However, if you're experiencing issues with the price not updating in the checkout page, there could be a few potential causes.
Firstly, ensure that the index mode is set to "Update on Save" for the Price index. You've mentioned that this is already set, but it's worth double-checking that this is configured correctly.
If this is already set up correctly, then the issue could be caused by other indexes not being updated. When you update the price of a product, the price index is updated immediately. However, other indexes, such as the catalog product flat index or the catalog search index, may not be updated until the next full reindex. This could cause the old price to be displayed in the cart and checkout pages.
To ensure that all indexes are updated when a price change is made, you can set additional indexes to "Update on Save". In addition to the price index, you may want to set the catalog product flat index and the catalog search index to "Update on Save". This will ensure that any price changes are reflected in all indexes immediately.
You can configure the index mode for these indexes by going to System > Index Management in the Magento admin panel, selecting the relevant indexes, and changing the index mode to "Update on Save".
If you've already set all necessary indexes to "Update on Save" and you're still experiencing issues with price updates not being reflected in the cart and checkout pages, you may want to consider checking your customizations and third-party extensions to ensure that they are not causing conflicts.