Issue when toggling between Mobile/Standard

I have a client who is reporting the following issue on their mobile site:
After landing on the mobile homepage, they clicked to view the Standard template. They then tried to click back to the Mobile template and instead of seeing the mobile homepage (which is specified in the "Homepage" field of the Mobile Joomla settings for each template) they are seeing a mobile version of the Standard homepage. Their Standard homepage is text-heavy, while the Mobile homepage is very clean, so seeing this Standard homepage in the Mobile view is concerning. 

However, I have tried to replicate this issue on both an Android and iPhone device and I'm not encountering the same issue. Can you think of any reason this would be happening? 

You are not the first who report this issue, but we cannot reproduce it too. Could you post URL of the site? And is System-Cache plugin published here? Do you have installed 3rd party SEF extension on the site?

Also it may be that client has pagination on frontpage and he switch to mobile version from page No.X (X>1) instead of homepage .

URL would be www.odysseycruises.com

System Cache is disabled. We're using the sh404SEF extension for URL management, but caching is disabled in those settings as well. 

Could you elaborate on your pagination idea? I tried switching over to Standard template from pages other than the homepage, and it seems to work fine. 

Was this ever resolved?  I'm having the same problem and it's obviously really not ideal!  Happened on the iPad.