13:11 was a 19sec PR for Filip and second national best. It is not SUB13 but very respectable ! 6sec faster than Jakob ! Despite the placing, it is world class and can be improved. He is only 26 . He can gain speed / endurance by training with his brothers any-day and by doing all the big races. In addition they do very little altitude training, compared to others. That might add a big bump to his perfs !
We have seen so many alterations in the past of a post race run. Salazar used mile repeats hours after races, following the idea, that your body is hyped up from a race. You can still perform greatly after a race and the hard training will not prolong further the already long recovery. So, why not just get in a workout and improve performance ?
Second option is, of course, you do your cool-down straight away after the race. However to have a kind of complete flush of the stuck byproducts you need another training session. It needs to be done on a special heart rate for each athlete for maximal benefits. Most likely they use Z2 mid / high efforts and a treadmill is the most controlled environment to follow that constant low HR. It might look like fast for an elite athlete, but in reality it is only Z2 !
Canova explains this in one of his papers too and the old Lydiard athletes practiced also an 8 to 10mile aerobic run the afternoon / evening after a 1500/3000/5000 race. You can read the "Running the Lydiard way" to find ideas about this.
Maybe it was only a post flight anti-jetleg jog ?
Can you share the link to the video ?