I think that even if your inbound flight arrives within the MCT you should still go to the gate for your connecting flight (at normal walking speed).

Because it might be hard to claim compensation, if for example they were holding the flight a few minutes to allow connecting passengers to make it.

If you then arrive at the gate and boarding is closed, then it's off to the transfer desk and also file a claim online ( depending on the reason for the delay of the inbound flight).