Manage Access is a security feature that applies to all screens, reports and functions in CORE, including time and expense entry. Project-level assignments also provides access to projects and items by specified employees. So, either one of the two must be in place in CORE because of which your employee is unable to enter time against that project. You need to either assign this employee to that project from the Projects > General > Assignment screen. Else, check the Manage Access screen (Settings > Access & Permissions) and assign that project to your employee to resolve the issue.