For COC (Convention Over Configuration) MAVEN has the four folders (java and resources for tests and main) in the classpath. If you didn't modify the pom.xml, using mvn from the command line will work.
In Eclipse, if you have the maven plugin (STS has it), you can right-click on the project->Maven (it has a bold red icon "m2")->Update project configuration. It will do the job for you.
Again, in Eclipse, you can do that manually with right-click on the project->Properties->Java Build Path, find the "Source" tab where you configure the "source folders on the build path". I don't recommend you to modify manually this option, it's better to let the maven plugin to do that, but if you're using another IDE without this plugin, it should have an option like that, in order to configure the output folder for the classes and resources (properties, xmls and so on)
There is an intermediate screen on the Push in...'s wizard that inform you of the target Java file.
Besides, you need to move all the related elements. If a method use an attribute (for instance, the *.aj integration tests uses an instance of the DataOnDemand), you need to select both the method and the dod variable and Push them in the Java file.
Furthermore, all the files involved in the "Push in..." operation need to be correct (I mean, they have no compilation errors) before performing the push.
Be careful with the Roo Shell. Sometimes it's better to operate with the shell closed, managing the files AND the Roo annotations, and then re-start the Shell.
These are good tips. If you want to be sure that code's not going to be lost when you do a push-in, there's a "Preview" button in the refactor dialog that shows you what the pushed-in code will look like. If you only see the source .aj file in this dialog and not the target .java file, cancel the refactoring and check the things listed above.