10x scale i a bit weird.

.obj doesn't store any unit system. When you work in cm in MoI, a box of 10 cm means 10 units. It's up to the .obj loader in Nvil to decide what to do with the unit (cm, m, mm etc).
If you create a 10x10x10cm centred box, working in cm in MoI, vertex should be between (-5.00,-5.00,-5.00) and (5.00,5.00,5.00). (.obj is a plain text format, so you can check it with a simple note editor).

So usually when you have scaling issue, it's often by 100, 1000 ... maybe Nvil default is decimetre ?

MoI have a few option if the export setting, like scaling factor, that can help to get a match MoI>Nvil ... but Nvil>MoI might still be off.

- Check if you can set NVIL default unit as cm (and check if there are any import/export options when it comes to unit conversion)
- Use .FBX (FBX format store the unit system, so loader can do a better scaling conversion)

"Save As" save the complete MoI scene, "Export" only save the selected geometries.