Should CiviMail report show bounces when using the Mandrill extension?
The first thing to check is that both the MTE extension and Mandrill are properly configured. For instance, are soft bounces configured to be returned to CiviCRM?  See here for instructions on configuration:  https://github.com/JMAConsulting/biz.jmaconsulting.mte

I believe bounces are passed on to CiviCRM's standard bounce processing. You may need to check that the bounce reasons and soft bounce thresholds are correctly set (need to do a little mysql magic for that though).

Remember that contacts are not put on hold until the soft bounce threshold is met.