Sorry to tell you this but yes it has delay and it's not the program. The graphics card on the Surface Pro 2 is simply not powerful enough to handle vector calculations which is why you see it make straight lines. It can't calculate the curves so it misses them and finishes the line without those curves so the line is straight. I have a Surface Pro 2 as well and it does not work with Animate.
I've owned dozens of Tablet PCs and while they're cool for doodling and hanging in coffee houses, they unfortunately have no real processing power despite what they try to tell you on the commercials and Animate needs that due a mixture of issues dating back to the macromedia days which Adobe has fixed in many ways, but the brush tool still stands as a difficult thing to make better in the program even on desktops, let alone a tablet.
In fact there's only one tablet at all that I've ever seen that can handle the vectors of Animate/Flash and that's the Cintiq Companion. You8 can currently buy them on eBay for about $1000 and while I'm sure this doesn't help you much other with your tablet, at least you know that it's not a bug, and it's not something Adobe can likely do about it.
Ah, thanks for the reply! I'd had my suspicions about this actually, since recently I tested drawing with my mouse and the issue still applies here, although not nearly as visible. It would seem I will have to use a different animation program for the time being, but I'm saving up for a Cintiq 13HD/22HD/27QHD Touch in the future, so I can use my primary PC in the future, and hopefully then I'll be able to dive into Animate CC without any problems.
As disappointing as this is, I can't say I'm surprised. Thanks again!
Yeah a 22HD works great but then it's really related to how good you graphics card is on the PC itself. An integrated graphics card still might not do the job which is essentially why the Surface Pro can't do it's job. You need a dedicated graphics card for Animate. Also for what it's worth I've read the 13HD has problems with cursor registration so you're probably better off saving for the 22HD
If you just want to animate, you might try Sketchbook Pro as it now has an animation timeline and while there's no sound you can still practice and even make finished animation with it.
Here's something I did using Sketchbook Pro's timeline feature.