It appears that ACE translator doesn't integrate information from different ODB++ steps when it exports Gerber files, is it correct?

ACE fully integrates information from different ODB++ steps, and support the full hierarchy of nested steps (if any), plus any additional object transformations & dcode transcoding (if required).  

ACE will export the Step (i.e Cell) that you select as the "Top Cell" to gerber.  Which ever cell icon has the "T" is the "Top Cell" to be exported.  You can select the "Top Cell" during the "Export Cell & Layers:" window (it appears after you have imported the ODB++ file, and before you select the export location).   

If you're unsure which cell is the the top cell, goto the CAD Viewer.. and select Cell Browser... (menu: View | Cell Browser..), and you can chose the "Top Cell" from there.