Hello @Colin_Besserer ,
In Project Online / Project Server Project Web App (PWA), to edit a project you have to check out the project, when you open the project to edit, it checks out the project. This is to prevent another user with the correct access trying to edit the project at the same time. After editing, you Save your changes, then if you want them visible in reports / PWA, you also Publish the project. Once completed, close the project and check-in the project. You wouldn't typically leave a project checked out to you if you no longer needed to edit it.
Hope that helps, Paul.