Avoid using Copy/Paste to move your Illustrator paths into Strata. When the path is copied to the Clipboard it is rasterized losing the Bezier controls.
When Strata pastes the data it does an autotrace-type function to convert it back to a path - but it will be a different path (even though it may have the same overall shape) with different Bezier control handles.
The preferred method is to Save your Illustrator file as an .ai file type. Then simply Import that into Strata.
Be sure your paths have either a Stroke OR a Fill, not both. Strata sees Strokes and Fills as separate objects and will create a new Bezier Region (from closed paths) or Bezier Path (from an open path) object for each. This can lead to confusion and modeling errors.