Regular communication is counselled, plus a dose of mutual respect:
313. In order to better benefit from the charisms and services of the ecclesial movements in the field of formation of lay people, we wish to respect their charisms and originality, seeking to have them more fully a part of the core structure which is present in the diocese. For its part, the diocesan community must welcome the spiritual and apostolic riches of the movements. Certainly, the movements should keep what makes them distinct, but within a deep unity with the particular church, not only in faith but in action. The more the wealth of charisms multiplies, the more the bishops are called to exercise pastoral discernment so as to foster the necessary integration of the movements into the life of the diocese, appreciating the wealth of their communal, formative, and missionary experience. A special welcome and appreciation should be afforded to those ecclesial movements that have already gone through examination and discernment by the Holy See, and are now regarded as gifts and goods for the universal Church.
Note the importance given to movements recognized by Rome. Not every movement has a universal stretch. Some are particular to regions within nations. What to do about these?
For deeper examination, an English translation of the 2007 document from the Aparecida Conference.