Also tried new structure with the "InstallWebSite = true" property setting. No errors. No web site.
, new Dir(@"AdminWeb\"
, new IISVirtualDir
{
Name = "MyWebApp",
AppName = "Test",
WebSite = new WebSite("NewSite", "*:8080") { InstallWebSite = true },
WebAppPool = new WebAppPool("MyWebApp", "Identity=applicationPoolIdentity")
}
, new Files(featAdminWeb, @"..\SetupIPAV\AdminWebSitePublish\*.*")
)