I'm not too sure how to split them up but you can customize the class that Mendix gives the tab by changing the name property on each tab.
For this tab, I gave it a name "secondTab"
and when I inspect it there is a class called "mx-name-SecondTab".
Hope this helps!
As addition to Austin McNicholas's answer
Name your tabs ftr-unique-page-name, (used ftr as shortcode for floatTabRight)
The above CSS selector will look for class names containing the "mx-name-ftr"
Another approach I have used when I needed to do things that tab containers didn't enable me to: Instead of tabs, create a set of action buttons and style those to look like tabs. This gives you a lot of flexibility in styling and placement that you don't have with tab containers. Each action button would call a microflow that would update an enumeration or set of booleans that control what is displayed on the page. An added side effect of this approach is that the last 'tab' selection a user had open when he last visited the page is still open, i.e. the 'tab' selection is maintained.