The default console handler is attached to the root logger, which is a parent of all other loggers including yours. So I see two ways to solve your problem:
If this is only affects this particular class of yours, the simplest solution would be to disable passing the logs up to the parent logger:
logger.setUseParentHandlers(false);
If you want to change this behaviour for your whole app, you could remove the default console handler from the root logger altogether before adding your own handlers:
Logger globalLogger = Logger.getLogger("global");
Handler[] handlers = globalLogger.getHandlers();
for(Handler handler : handlers) {
globalLogger.removeHandler(handler);
}
Note: if you want to use the same log handlers in other classes too, the best way is to move the log configuration into a config file in the long run.