I just tested your page in the latest versions of:
- Safari: iPad
- Safari: OSX
- Firefox: OSX
- Chrome: OSX
- Chrome: Android
- Chrome: Windows
- Firefox: Windows
- Internet Explorer: Windows
- MS Edge: Windows
Initially on these browsers the tabs worked as expected for me with no page refresh required, however as you mentioned that you see the issue when switching between pages with tabs I then looked for other pages on your site that used tabs and found that when navigating between these pages the tabs are shown as headings and divs when the page first loads, but the tabs are shown when the page is reloaded. This is not an issue I have seen before, but I think a possible cause of this would be that something is preventing the tabby jQuery script from being processed in the browser.
To troubleshoot this, check whether it still occurs when all other plugins are temporarily deactivated, and also if the theme is switched to a default theme such as twenty-sixteen. Testing again after enabling the theme or each plugin should indicate which component has a script which is preventing further scripts from executing.
