An update to the TIF Reader app (version 3.0.1) has been published to the App Store that fixes this issue.
When updating TIF Reader from version 2.2 to version 3.0, the Recent Files list may reset to empty.
As a workaround, you can roll back the version of TIF Reader on your device to access TIF Files in your Recent Files that may not be visible in version 3.0.
1) Open the App Store app
2) Navigate to Updates, then tap Purchase History
3) Search for TIF Reader and tap the iCloud download icon. This will restore your app version to the version you select (2.2).
*Note* If you have deleted the TIF Reader app after updating to version 3.0, your files were also removed when the app was deleted. In this case you will need to locate the original source of the TIF file and open it into TIF Reader again.