Azure Search Switch On Rebuild feature is only relevant for the full index rebuild. When configured correctly, it tells Sitecore to perform index rebuild in a new index while keeping the current instance as the primary index. Once the new index is fully built, Sitecore will switch to the new index and make it the primary index, then the old one will be removed.
Behaviour you mentioned is not connected to the Switch On Rebuild functionality because updating, creating, deleting and publishing items trigger incremental index updates rather than full index rebuild.
Depending on how your indexes are configured, these incremental changes can be processed synchronously, asynchronously, based on an interval, etc. You can read more about different indexing strategies in Sitecore documentation here.