Yes, looks like a bug. I’ll submit this as a defect to support@axure.com . (Pinging @Chelsea_Axure to see if support can chime in here, but official means is sending an email or using Help > Submit Feedback or Bug.)
I would not expect hiding and showing a dynamic panel when using the mobile previewer would show a standard “non-mobile-preview” scrollbar style.
Given this is the case however, I recommend you use the approach on Page 2. Changing dynamic panel states is a more reliable way to implement a tabbed structure. I also simplified the code for the tabs by assigning them a Selection Group so that only one may be selected at a time.
To demonstrate the issue clearly, I added a Show/Hide button to Page 2. When a scrollable dynamic panel is hidden then shown in a mobile preview (page dimensions assigned) the standard scrollbar is used instead of the “mobile preview scrollbar” style.
To show how dynamic panel scrollbars look in a standard web page view (no page dimensions assigned) I added a Page 3.
Scrollbar Bug.rp (5.4 MB)