You can check out my site at http://fixmygateaustin.com and in mobile view the hamburger icon displays the default menu of “Home, Work, Shop, About,Contact” instead of the Primary Menu that I have it assigned as.
You can see it in this screen shot. 
But when I check it on my phone or other people check it, this is the menu it shows: 
PLEASE HELP!
Hello There,
Thanks for writing in! Please edit your header and make sure that your navigation inline and navigation collapsed elements are using the same menu. You might have used the default or assigned a different menu in the navigation collapsed element. And by the way, since you have installed a caching plugin W3 Total Cache, please clear your plugin cache before testing your site. This can cause the changes to not take place on the front end. It will eventually show up when the cache regenerates, but it’s not ideal if you’re looking to see your changes immediately. Caching plugins are best to turn on only when you’ve finished building the site.
Hope this helps. Kindly let us know.
Thank you so much, that worked!
On behalf of my colleague, you’re welcome. Cheers!