Will this method work with email submits/cpa offers, or have you only had success with amazon links?
Also, what kind of traffic does a new tumblr generate? does it need any promotion or is it jus recycled traffic through the tumblr network?
Yes, it works with CPA. I'd recommend using something relevant to content.
A new tumblr is usually hard to get off the ground, but if someone popular reblogs your post, you can easily get a few thousand people clicking your link. Things go viral very quickly on Tumblr, thats why you have to keep experimenting with different tags and niches. You will mostly get recycled traffic from users already on Tumblr, but you will also get Search Engine traffic because Tumblr posts rank pretty good for long tail keywords.