Let's describe the issue with a test. Assumming we already have an injector and a JenkinsController, the following test will fail:

Jenkins j1 = new Jenkins(injector, jenkinsController);
FolderItem f = j1.jobs.create(FolderItem.class);
Assert.assertSame(j1, f.jobs.getJenkins());

The problem reproduced is the same described in JENKINS-37615, but specific to {{FolderItem}}s, since they are not properly receiving their context when created.