What's the physics behind this plasma generation ?

We understand plasma as the 4th state of matter, where the matter is hot enough that it is constantly shedding it's electrons.

With the match in the microwave, the air directly around the head of the match is very hot when the match is lit. Since there is water vapor in the air, the water vapor around the match is also very hot already. The microwaves emitted are designed to excite water molecules in the food, that's why the food heats up.

Well, since the lit match is already exciting the water molecules in the air directly around the head of the match, the microwaves provide enough energy to the already excited water molecules in the air to kick them up to the 4th state of matter. This is also why when the microwave stops, the plasma immediately disappears -- because without this radiation excitation, the plasma cannot sustain the energy to maintain the state, and the electrons almost immediately go back to where they should be -- around the water molecules.

A bit long winded, but hope this helps.