Once you have added a SharePoint task list to Project Web App, it is displayed as a single project row in the Project Center. Clicking the name of the project in this view opens the SharePoint site that contains the list.
To view the task list itself, click once in the left column for the row to select the entire project row, and then, on the Projects tab of the ribbon, in the Project group, click Open, and then click In Project Web App.
Note: If the task list is currently only visible in Project Web App, if you click In Project Web App for Editing, the project still opens in read-only mode. If you want to be able to edit the project in Project Web App, see Change a SharePoint task list into an enterprise project. If you want to make edits to the task list, you can do so in SharePoint, or by using Microsoft Project Professional 2013. For more information about this option, see Edit a SharePoint task list in Microsoft Project Professional 2013.