The issue is the mirrors not the handlebars.
Looking at the link you supplied I cannot see clearly how the vertical piece that holds the mirror clamps to the horizontal piece that inserts into the bars but it looks like its two smooth surfaces that simply hold with friction which is never ever going to work. Personally if that is the case I would toss them or try to return them and get something that is better engineered.
If you do want to persist try putting something between the vertical and horizontal pieces that provides a surface for the vertical piece to get a grip of. That could be something like gaffer or duct tape or even glue. It may work I suspect to won't.
Looking at the link you supplied I cannot see clearly how the vertical piece that holds the mirror clamps to the horizontal piece that inserts into the bars but it looks like its two smooth surfaces that simply hold with friction which is never ever going to work. Personally if that is the case I would toss them or try to return them and get something that is better engineered.
If you do want to persist try putting something between the vertical and horizontal pieces that provides a surface for the vertical piece to get a grip of. That could be something like gaffer or duct tape or even glue. It may work I suspect to won't.