You can mirror your iron on vinyl in the prepare screen in cricut design space and if you select iron on vinyl as your material there will be a warning reminding you to mirror your image.
Cutting the wrong side of iron on vinyl.
Tips for weeding iron on vinyl.
And here is the vinyl side which you can see is matte not shiny.
For iron on vinyl you want to get the mirror image it s not important unless you have text or an image you need to face a certain direction.
You need to place iron on vinyl shiny side down on your cutting mat then mirror the image for cutting.
Here s the two sides of cricut everyday iron on vinyl here is the carrier side of the iron on vinyl which you can see is shiny.
You mentioned the image is sticking to the iron so it sounds like you might be cutting the vinyl sheet wrong side down in the machine.
So in the above case you d want to put that iron on vinyl shiny side down on your cutting mat to cut out your mirrored design.