Will my 3d tour be on realtor.com automatically?

No, you have to click "publish tours to listing on realtor.com" to have the 3D tour visible on realtor.com.

The difference between posting a virtual tour from MLS and from the Asteroom app  

Posting a virtual tour by synchronization of realtor.com and MLS will have a "Virtual Tour" button and badge on the listing on realtor.com, but no "3D Tour" button and badge. And when you click the button, it will open in a new web page. This will make it less likely someone will become a lead for your listing.

Posting a virtual tour right from the Asteroom app will have the "3D Tour" button and badge on the listing, and it will open the virtual tour in the same web page. The best way to get rid of the MLS's link restriction and increase the likelihood of buyer leads.