When and how in anaerobic digestion is water dissociated?
This is not a trivial question to answer, as many diagrams are often simplified and do not state the full chemical reactions that occur, such as



from Aerobic and Anaerobic Digestion and 
Types of Decomposition education webpage from the Mountain Empire Community College.

However, according to this image (below) from the Ecocorp page - Metabolic Chain of the Anaerobic Process for the Utilization of Organic Wastes, water is a reactant in the acetogenesis
 stage and is removed as a product in the methanogenesis stage.

(Sample reactions are included in the image)



(Just in case the image becomes a dead link), the chemical processes involving water from the diagram are:

acetogenesis

$$\ce{CH3CH2COOH + 2H2O -&gt; CH3COOH + CO2 + 3H2}$$

methanogensis

$$\ce{4H2 + CO2 -&gt; CH4 + 2H2O}$$