Incremental training and Auto Machine Learning for big datasets
First of all using auto-sklearn, you can use

automl.fit(X_train, y_train, dataset_name='X_train',
               feat_type=feature_types)

    print(automl.show_models())


so you can extract the instance of the best model from the first fitting. However in order to learn incrementally you have to (in case of sklearn models) have fit_partially method. Naive Bayes varaints and other algorithms here have this functionality. So you are out of luck if these are not in the output of show_models: In this case you ought to do your own automated ml targeted on fit_partial models.
Alternative is using spark it has some cool streaming (incremental learning algos)
StreamingKMeans, StreamingLinearRegressionWithSGD, StreamingLogisticRegressionWithSGD and generally StreamingLinearAlgorithm.
To conclude, I would not use auto-sklearn if these are your problems and choose some alternatives that do work parallel.