The easiest way to control the roughing area is by controlling where the stock is.  Even if any small amount of stock is found, the procedure will try to take a skim cut.  This may not be desirable.  There are 3 effective ways to control where Volume Milling cuts:

1)  Boundary.  We can define a boundary to contain the path.  The only downside to that is that now it will want to cut the top of the internal island.  That leads to option 2.
2)  Minimum Stock Width.  Set the value high enough and it will ignore any small remnant stock on the top of the part.  This option is found under tool trajectory.

3)  Multi Groups.  While we don't have check surfaces in Volume milling, we do have Multi-Surface Groups.  Since Volume Milling cuts stock up to a part face we can use these Multi-Surface Groups to our advantage by creating a second group and increasing the part offset until the cutter cannot engage the stock that might be on the part surface.

Any of these options should help, but starting with the stock definition is key.