Excerpt from an e-mail I received back from MPC on an (eventually successful) attempt to use an upgrade certificate:

"I regret that our staff was not able to
explain the conditions of use of the Upgrade Certificate clearly. Allow
us to clarify that the certificate needs to be presented when you
approach the check-in counter. The seat controller will then process the
upgrade according to the booking status and seat availability. You will
receive the upgrade immediately if the flight is not busy, otherwise,
the outcome will be given at the boarding gate."