Hi,
I looked at your code on codepen. The jumping is caused by the SVG treating the hash tags purely as an anchor tag. For example, if you make that bottom div 2000px high (so there's plenty of room to scroll), you'll see that clicking on one of those shapes will bring you right to the anchor.
The active class not being added is probably to to with how classes are added in SVG's. It's different than 'normal' elements in an HTML doc.
This is what I would consider a tinkering job :-) I can get it to work, though I'm not sure exactly how I would do it. My first shot would be to try creating intermediary javascript functions that acted between the SVG and the tabby script. In any case, that's why I've bid outside of your range, I think it's going to take some time experimenting to get this working.
Thanks and hope to hear from you,
John