As explained here and elsewhere, you can develop both web and native applications with Tersus.
Native applications are based on a bundling of Tersus and PhoneGap. Esentially they are modelled in the same fashion as web applications, and ultimately exported via the export wizard which packages together the Tersus application, the generic Tersus client and the PhoneGap library and creates a xCode project (in the case of iPhone - see here) or an APK executable (in the case of Android, and assuming the SDK is installed - see here).
Regarding your dialog woes, they should be fixed in the next version 2.0.10, at which time we shall updated the tutorial as well. In the meantime I suggest that you always specify a <Scope>, passing it a reference of the display which you want the dialog to replace when open.
For best results, use the Firefox browser..