Either published workbooks with embedded extracts or published data source extracts can be refreshed. If your Server can access your local data, it can pull the updates manually or on a schedule using the embedded credentials. If not, you can push them from Desktop using the refreshextract command described earlier in this thread.
How can I test to make sure that it has access to refresh my local extracts? Like I said, I have embedded my credentials everywhere and the refresh task on the tableau server said it went well. I think the issue is that my extract is not pulling from my data source.
Best way to test is to install Desktop on the Server machine, and test the refreshes in Desktop, not using your own account, but the account that is used by Tableau Server. That's one extra thing that can get you, see the following link.
But if Tableau Server says the refresh went well, it probably didn't have trouble with the data path or credentials.
Can you add some more details or screenshots showing what you see?