Just in case someone will encounter the same problem, here is the solution for my problem.
In order to let Adobe Target measure conversions based Analytics metrics, you will need the Adobe Visitor ID Service (I had it running). But you will have to ensure that Visitor ID Service is being loaded before Target (this is where my problem was).
1. Adobe Visitor ID Service 2. Adobe Target 3. Adobe Analytics
I just wanted to share my solution if someone will have the same issues.