Generic Model families can be a bit overbearing when it comes to visibility.  Unfortunately, you can’t usually change the Show only if Instance is cut property for Generic Models… unless you switch them to a Category that allows this to happen, like Windows.

Andy Milburn describes it thus:
“With a window family this is easily solved by checking the “only show when cut” box. In a generic model family this feature is greyed out.

You will have already guessed my solution. Swap the type to window, check the box, swap back again to GM. It stays checked even though it’s greyed out.”

EDIT Current category guide post:

In Revit, some families have Cut Dominance, some are Cuttable, and some respect various View Range rules in various ways.

These behaviours may further be affected by the Family Template that they were created from, whether they are Hosted or non-Hosted, whether they are Shared or not Shared.

Wouldn’t it be awesome if there was a document that went through each Family Category and described its unique properties!  I have asked Autodesk for this before, but to no avail (SR# 1-9298685321 – The help file does not describe the unique properties of each Category).

Andy Milburn shares my feeling on this matter:
… I wish I know where to find a clear explanation of all these rules.
Shades of Grey: CUT ! CUT ! CUT !

What about the Families Guide?

I may not have all the answers, but I have posted many times about the differences between certain Family Categories.  See some links below:

Cuttable vs Non-cuttable Family Category Properties

View Ranges (and TOLERANCES) Explained *REPOST*
Things like –
Walls shorter than 6 feet (approximately 1.83 meters) are not cut, even if they intersect the cut plane, and
There are a few categories for which an element located above the cut plane but partially below the top clip is shown in plan. These categories include windows, casework, and generic model. These objects are shown as viewed from above.

Project Family Category Type Instance
which Categories do not have Types, or which Category has Types but no Instances?

Making unhosted components like unhosted Doors and Windows

Create a Component Family with Category set to Walls (or other system family category)
Yes, it is possible.

Plan regions have no effect on Topography – workarounds

buildz: Wall Trimming Method
Cut Dominance in action

Have you struggled with the Show only if Instance is cut option in the family element visibility settings.  Was it grayed out?

The following highlighted categories (wall hosted) have ‘Show only if Instance is cut’ option enabled, at the moment in Revit Architecture 2012.

Structural Columns
Structural Foundations
Structural Framing

Revit Sticky Notes: 2D Symbolic Line & ‘Show only if Instance is cut’
(includes workaround)

One easy way to determine if a family Category is Cuttable is by looking in the Object Styles dialog box. If there is a gray box in the ‘Cut’ column, that Category is not cuttable. See image below (from 2012):

For some further info, you can check out these WikiHelp pages:
Cuttable Families – WikiHelp

Non-Cuttable Families – WikiHelp
However, it would seem that the above lists are not exhaustive…

Also, you can check out my previous post about the subject:
What Revit Wants: Cuttable vs Non-cuttable families

You want to know which families are cuttable and which are not.  Revit 2011 help gives the answer:

Cuttable families (link):
Curtain Wall Panels
Generic Models
Structural Columns
Structural Foundations
Structural Framing

Non-cuttable families (link):
Detail Items
Electrical Equipment
Electrical Fixtures
Furniture Systems
Lighting Fixtures
Mechanical Equipment
Plumbing Fixtures
Specialty Equipment

What is a cuttable family?

If a family is cuttable, the family displays as cut when the cut plane of a view intersects that family in all types of views.  From Revit 2011 help.