You can check the syndication status of your listing from the Zillow Rental Manager's "Listing Status" tab.
Syndication is not immediate, each post is run through a verification process to confirm its location and content. It can take up to 2 hours for a listing to appear on Zillow and Trulia, but is usually up much faster.
If you have incomplete or inaccurate information (e.g. you don't include the full address), your listing may not be processed. If your listings are also syndicated from another source, that may also interfere with syndication from Zillow Rental Manager as only one version is posted on Zillow.