Are the "double curves" two identical paths stacked directly on top of each other? That's something I see frequently with artwork imported from customer provided PDF files. Sometimes the duplicate paths have no fill and no stroke. But a vinyl cutter will certainly cut those invisible paths anyway (obviously it's not good for a plotter knife blade to cut 2 or more times over the same spot on a roll of vinyl). It's very important to "police" imported artwork that will be sent to a vinyl cutter or routing table. Plugins like Vector First Aid can automatically eliminate things like invisible duplicate paths.
Another issue is how vinyl cutters (or routing tables) will interpret vector shapes that have line strokes. Does the converted text objects have line strokes in addition to fills or just line strokes only? Exported artwork may be imported by a "CAS" application such as Flexi or SignLab with the line strokes expanded into parallel editable paths inside and outside the original path. A knife blade or router tool bit will cut where ever a path is present. If I'm creating artwork that will be sent to a vinyl-only cutter/plotter machine or a routing table I'll give the shapes a solid fill with no line strokes at all.
Then you have other exceptions like large format printing where the RIP software will do print-only and cut-only operations, like contour cutting a large format print that has been laminated. This artwork needs a cut path defined (typically with a custom spot color and name, such as CutContour); those paths are usually given a thin stroke and no fill.
Variable Fonts are another possible issue. Some but not all Variable Fonts will have letter parts that overlap. The areas that overlap will be visible in Outline View after the text has been converted to outlines. The overlaps must be welded (such as using the Pathfinder Unite command) to remove the overlaps before sending the job to a vinyl cutter or routing table.