There are a number of ways to turn straps and tubes inside out, but it can be hard sometimes, especially if they're really skinny. This super-helpful step-by-step from the blog Handmade Things is the easiest way I've found to turn skinny tubes (like spaghetti straps or button loops) right side out.
I used this when I was making button loops for a top for my nieces.
|I ended up hating the top--but loved the buttons!|
Basically, you sew your tube, leaving both ends open. Then you cut a small horizontal slit just below the opening on one end. Stick a bobby pin with one leg through the slit and one through the main tube (it may take a little wrangling). Then you can slide the bobby pin through the tube and the other end will follow. Let me know if you try it, I think you will find it works better than other methods!