Hi guys, thank you so much for the quick answers and apologies for the late reply, I didn't have e-mail notifications on and didn't expect such swift answers. Much kudos for you guys.
Indeed Diaco, your answer was absolutely right. First I had my text styles on the P tag, but as this is changed into multiple DIV's when handled by splittext, which made them lose their styles. In my train of thought it was logical to redeclare those on the DIV, causing my problem. Now I declared them straight on the .quoteHero__quoteContent and everything works like a charm.
Thanks again, I really enjoy working with greensock, and knowing the support is this great makes it even better.
edit: While I'm at it, I've got something I can't seem to reproduce on Codepen. On my localhost the codepen example is part of a slideshow. The first loads in plain html, the next ones are loaded through ajax. On first load the lines still aren't broken on the right points. When I ajax load the next one they all animate fine though. When I add a timeout to the animate function it works fine as well. Is that something that sounds familiair and might have an easy fix?