From the Web Tools team:

1.   I’ll add a new IVSHierarchy property called VSHPROPID_ActiveIntellisenseProjectContext which will gets or sets the project name of the active intellisense project. This  string will match the value returned from ICSharpProjectRoot::GetFullProjectName.
   

2.   IVsHierarchy events will be generated when this property is changed just like when VSHPROPID_SharedItemContextHierarchy is changed
   

We need to consume that new property.