I started a little blog on Tumblr a while ago now. This was mainly to try it out, and also to keep a record of unusual, interesting articles that I found on the web.
While it is an elegant tool, and very user friendly, it certainly takes a long while to get indexed. I thought it might happen automatically, since this does seem to happen with other platforms. (That is, when someone creates a site, there often seems to be some sort of automatic listing of it on the main site, and that qualifies as a backlink.) But this process (or something like it) seems not to have happened here.
In any case I did create a backlink weeks ago on one of my blogs. It still hasn't kicked in. So, this does seem to be a bit of an issue.
And this experience does seem to concur with other assessments of Tumblr. I have read repeatedly that it is not easily and quickly indexed by search engines. Here's an example.