By default, the Dialogue System uses Unity's standard Input to check the state of input buttons. To use a different method to check input buttons, assign a delegate method to DialogueManager.GetInputButtonDown. This is what the Rewired Support package does.
To temorarily disable input to the Dialogue System – for example, if you open a settings menu – call DialogueManager.SetDialogueSystemInput(false). If you're using UnityEvents, you can hook it up in the Inspector as DialogueSystemController.SetDialogueSystemInput.