There's 2 ways of attaching images here. The standard way (which you are familiar with), places the image(s) underneath your post.
The second way is called inline attaching. To do this, you upload and attach the image(s) exactly the same as you're already doing. Once attached, hit the paper clip icon again, and click on the file name you uploaded. That will insert the image (with the [attach] tag) wherever your cursor is in the reply window.
Example:
If you uploaded multiple images, you'll also see an "insert all" option after ticking the paperclip, which will insert all attachments wherever your cursor currently is, with a line break separating them. Once you have the [attach] tag in your post, you can obviously cut and paste that text to reposition the image(s) wherever you want within your reply (if it wasn't exactly where you wanted it to appear).