Thanks in advance!
What I want to achieve is to open the popup window when a special tag is detected on a webpage by my extension. After searching for a while it see
If by popup you mean browser action popup then you are right, there is no way of opening it programmatically.
You can embed whatever you need from your popup on demand directly into a page through a content script. I think this would be the best solution.
If your popup doesn't contain anything fancy, maybe desktop notifications would be enough for you.
Creating a new window and positioning it under the url bar would be pretty awkward solution and not very user friendly.