As I see it, If the project is created with a 16:9 preview but exported 9:16 it will letterbox or pillarbox scenes as needed to fit the format. Others may disagree.
Outputted at 1920x1080, your film's first clip fills the screen while other scenes are vertical. They look good on my 24-inch PC monitor. Your viewing device may allow adjustment to taste. You might also test lower-res 16:9 exports to see how they look on your target device.
At that res and aspect ratio, when viewed on a horizontally-held 7-inch tablet, vertically oriented clips filled the screen top-to-bottom, and aspect was correct throughout. Nice presentation. When exported at 9:16 the result was as you described - either a narrow band or pillarboxed. Aspect ratios seemed to be okay.
If you want an export that displays larger, vertically, on a phone or tablet, before editing you can right-click the VP preview window and Change Preview Settings to 1080x1920 (9:16). Then crop/position/scale your edits for that display and export at the same setting.