They are burning tires or other garbage in a cooling tower, from what I have gathered. They are pretty far from the main containment facility, especially the reactors, which I believe are in shutdown now. If so, the cooling towers aren't being used if the plant is in a standby state.
There's not much inside a cooling tower to damage or catch fire. If you've ever seen pictures inside one, or seen the movie Brazil, it's just a network of radial steam pipes that make up a "floor", with holes in them to let the steam out. The platform of pipes is raised about 20-30 feet from the actual ground below. Nothing particularly flammable about it.
Other than maybe a few small valves, pumps or other actuator type control equipment, there is not much that's either electronic or particularly sensitive inside them. The walls are reinforced concrete, AFAIK, and they also are not flammable.
Although Putin might be embarrassed, he won't deliberately risk an accident there. It would cause too much blowback and they would be risking nuking themselves, essentially. But, there is always the possibility of an accidental shooting or explosion that can happen, and neither side wants that.
Building a tire fire inside a cooling tower is either because the troops there are bored, or it might be their way of trying to act threatening - but anyone with a little knowledge of how the plants work will not be easily fooled.