openmpi3 changed the way it has to be told to use only one core and it will fail if you don't take care of setting this appropriately on autopkgtests.
The solution is to add the following (or equivalent) to the test script.
An example bug where this is discussed is bug #850229.
The error that you'll see is something like (phyml 2018-06-27)
There are not enough slots available in the system to satisfy the 2 slots that were requested by the application: /usr/lib/phyml/bin/phyml-mpi Either request fewer slots for your application, or make more slots available for use.