Backlinks from Tumblr not being indexed

It's not normal for a Tumblr to take more than a month to index.

There may be many reasons for this -

If the Tumblr was spammed before then there is a chance of this happening.

If there are lots of links from a newly created Tumblr blog, then Google may just decide not to index it.
Kindly wait for few more weeks, if still not indexed, we suggest you move on to a new web 2.0 other than Tumblr.