In fact, when we moved to Logback for the Server's own log, we decided to keep log4j on the existing example adapters.
This reduced the overall changes and reduced the coupling between the Server and the examples; note that the logging libraries included are visible globally and that the in-process java Adapters are not protected in their own ClassLoader, hence, the logging libraries can be accessed by the Adapters; however, the logging system was not meant to be part of the java Adapter interface.

When the Adapters were able to share the logging system with the Server, there were no initialization issues.
On the other hand, if the Adapters only share the logging system among themselves, we have to ensure that the initialization is performed in the correct sequence, as the Adapters are all initialized in parallel.
By replicating the log4j initialization (as done in init(), in ChatDataAdapter.java) in all Adapters, we have never noticed issues. Actually, our log configuration files are very simple; we just ensured that they would define the same appenders in the same way and that they would all define different loggers.
Is it possible that you define the same appender in different ways on different files?