maven can't add files in generated-sources for compilation phase

In my understanding, maven 2 automatically add generated sources, is that right?

Nothing automatic, plugins generating source code typically handle that by adding their output directory (something like target/generated-sources/<tool> by convention) as source directory to the POM so that it will be included later during the compile phase.

Some less well implemented plugins don't do that for you and you have to add the directory yourself, for example using the Build Helper Maven Plugin.

And since you didn't provide any POM snippet, any link, I can't say anything more.

And what if my testing code also depends on the generated-sources, do I have to manually specified the compiler includes?

As I said, generated sources are usually added as source directory and compiled and are thus available on the test classpath without you having to do anything.

Generated sources are not compiled or packaged automatically. Some IDEs (i.e. IntelliJ) will however show them as source folders.

To make generated sources visible to maven add a add-source-step to the build/plugins node of your pom.xml:

<plugin>
    <groupId>org.codehaus.mojo</groupId>
    <artifactId>build-helper-maven-plugin</artifactId>
    <version>3.0.0</version>
    <executions>
        <execution>
            <phase>generate-sources</phase>
            <goals>
                <goal>add-source</goal>
            </goals>
            <configuration>
                <sources>
                    <source>${project.build.directory}/generated-sources/gen-java</source><!-- adjust folder name to your needs -->
                </sources>
            </configuration>
        </execution>
    </executions>
</plugin>