Peter,
The Autocomplete-Polygon editing task works only on the assigned target feature class containing the polygons so no mistake or bug there.
I suppose that answers your question and you may already have other means of dealing with the consequences:
However, there are many simple ways of handling the separation of features created in one feature class into others.
The simplest way for your work flow, as I understand it, would be to continue digitizing the field and dams together using autocomplete to maintain common boundaries but:
1. assign a distinct value to the dam polygons made in your Crop Fields FC
2. at some point open the Crop Fields attribute table and use the select by attributes function to select all the polygons with the dam attribute you assigned (or just pick them with the edit tool)
3. change the EDITING functions to TASK: Create New Feature and TARGET: Farm_Dam FC
4. use the edit tool in the Data View and transfer the polygons to the Farm_Dam FC by the following:
4a. right click "COPY"
4b. hit DELETE (or right click and "delete")
4c. right click "PASTE".
That sequence will cut the dam polygons from the Crop Field FC and create them in the Farm Dam FC where you can then edit their attributes.
... Numerous other ways of handling all this including splitting the polygons with dams, not using Autocomplete and starting with just polyline outlines etc. ... All fairly standard editing procedures.
Hardolph