I was looking through Google search engine and I know that for every search, there is this 4 'options':
Show Google's cache of www.thinkingincome.com
Find web pages that are similar to www.thinkingincome.com
Find web pages that link to www.thinkingincome.com
Find web pages from the site www.thinkingincome.com
Find web pages that contain the term "www.thinkingincome.com"

I found no backlinks. But I do find my website's 'links' when I click on the last one.

I found webpages that have my website listed and they are the ones that I submitted my directories.

Am I correct to say that these pages found will become actual backlinks in the next Google update?

they probably already are. If it's a <a href="..."> on the page, indexed and cached it's a backlink.

Google shows just some of the links, so dont't warry you have the links but they are just not showing on google... I dont know why is it so... any ideas?

@ nkthen

you have to wait, google will show all the backlinks after a while

I think Google should remove or hide the backlink feature. For the average site, it doesn't display any backlinks. Generally, it will only display backlinks from really major sites (which don't tend to link to the average site).