Shopify Marketplace Connect publishes updates immediately, however, these updates typically take between 5-60 minutes to be processed by the marketplace. This includes inventory edits from Shopify to the marketplace (e.g. more goods received).
If you have fast-selling inventory, consider using the Quantity Buffer option in the inventory field to reduce the risk of overselling. For further inventory information.
For further information on inventory using listing modes
For further assistance, please reach out to marketplace-connect@shopify.com