The Algolia Shopify extension automatically keeps your data up to date using Shopify webhooks - to know when you make updates to your Shopify catalog, and to immediately pushes the changes.
We do not have an integration with Salsify at this time and we do not support Salsify.
While you can use Salsify to manage your products/inventory, you would need to make sure that Salsify's updates properly trigger Shopify webhooks.