How does VBR mp3 bitrate is specified?

It doesn't actually need to be specified. Each frame contains its own bitrate (as shown in that site Customsex linked). However, there can be a custom Xing VBR header on the file that helps apps track their position in a VBR file. The empeg requires this special header in order to properly track into a VBR file. I'm guessing that your ID3-writing library is clobbering this header. There are available tools that can repair the header, I'm sure some of them are open source.