Fine, you may not be aware of the meaning of the term indexing. Indexing in SEO refers to search engines keeping a record of your web pages. When working on indexing of your site, you should target all major search engines (Google, Bing, Yahoo etc).
I'm sure, it will take some time to get indexed. If you want it will index automatically so for that you have to post quality content on your Tumblr blog and you should get a good number of visitors on that blog.
Usually when a search engine bot comes onto your site, it starts crawling and, based on "index" and "noindex" meta tags, it adds pages with index tags in that search engine. Apart from onpage SEO optimization like meta tags, meta keywords, meta descriptions and on-site SEO (noindex, nofollow), I used robots.txt to put the websites into search engines in just a few hours.
Robots.txt refers to a standard used by websites to communicate with web crawlers and other web robots. Before you try to index a new website, make sure you have your content prepared, because you don't want Google bots to come and crawl your empty homepage. Hope it helps for you. Thanks - BB