Certainly the plasma could melt the wall if it were allowed to touch it, but by shaping the magnetic fields that confine the plasma, the plasma can be made to stay away from the wall (not perfectly, but well enough). This is how many fusion experiments operate today. The walls are made of tungsten and other materials that can handle heat, so even if (when) the plasma hits the wall, the melting isn't too severe.

Some "plasma touches wall" events are more severe than others. Sometimes it's even intentional. A "limited" plasma deliberately touches a part of the wall called the "limiter", and the limiter is used to bound the shape of the plasma. (Contrast with a "diverted" plasma; search both terms for more details.) On the other hand, one type of event where it's very much unintentional is called a vertical displacement event, in which the plasma, well, vertically displaces itself until it hits a wall and melts it. These suck but are planned for and handled.

If you're counting neutrons in that "energy flux", they'll just go through the wall (mostly); this is how tokamaks are supposed to make electricity, ie the neutrons go through the wall and hit a "blanket" that's much better at absorbing neutrons, and the blanket will heat up and the heat will be converted to electricity.