the error you were gettings is because the constructor in your second class needs to be "public", meaning:
Code:public class ClassInATab{
public ClassInATab() {
System.out.println("ClassInATab constructed");
}
}
however, classes in additional tabs are just embedded into the main class that's defined in the first one. this is so that the rest of them still have access to all the processing functions (line, fill, etc).
in java mode, however, this won't work, because the class is already closed off, so after fixing the problem above, you're just gonna confuse the preprocessor.
the only way to make classes that are *outside* the main applet class is to create a .java file, which will not be preprocessed at all. so when you make a new tab, add .java to the name, telling processing to just read the code as straight java.
all that said, the better way to do it is to take the first tab out of java mode, and things should work fine. assuming you don't have a problem with ClassInATab being an inner class.
fwiw, there's not much use for java mode anymore, since import statements now work properly.