No, you don't have to set up a new class for each view, but you probably will need to assign new attributes for the class for whichever view you're in.
Since you didn't provide a sample link, I'm just basing this on assumptions. Here's an example that maybe will help you "get it."
Let's say in desktop mode, you have a headline font (assigned class: "headline") that is 72px and is centered on one line and has a top-margin of 200px to push it away from the top. Positioning looks great.
When you go to your tablet mode, the top margin has pushed it too far down the viewport, and now your text is too big for the screen and pushed onto three lines that are too close together. It all still has a class of "headline," but you need to adjust your font size and margin (and possibly your line height) to make it look good in that particular viewport. Let's say you change the font to 60px, and maybe adjust the line height, with a new top margin of 100px, and it looks great.
You didn't assigned a new class. They both still have a "headline" class, but the attributes at the different breakpoints have changed. Webflow writes this code for you and remembers it from break point to break point (the points at which the desktop switches to tablet then to landscape phone then to portrait phone).
Same thing happens when you go to phone view, you'll have to make attribute adjustments for the "headline" class, but you don't have to assign a new class.
Here's something important to remember... the attributes you make on the desktop view "flow down" through all of the viewports to the phone view. If you change the tabet view, that change flows down to the phone view as well, but the desktop view retains its attributes. Just remember, the attribute changes flow from largest to smallest view, but they don't flow up.
Hope this helps and makes sense. Good luck!