What is the counterpart English word to Japanese word, “Match-pump”?

When I was posting a question about the difference between “Strike a match” and “Strike the match” today, I recalled a made-in-Japan English compound, “Match-pump,” which means a person who instigates others to do something, e.g., to call a strike, or make a fuss, and scurries about to stop or quell the subsequent movement / commotion when the matter gets serious. Pump in this compound means water-pump.

In other words, it means the person who strikes a match to burn something (in a fun more often than not) and tries to extinguish a fire when it flames up.

I wonder if there is the English word that purports the same meaning in a single word.

There's a psychological "condition" named Hero's Syndrome which is apparently relatively common among firemen.

The hero syndrome is a phenomenon affecting people who seek heroism or recognition, usually by creating a desperate situation which they can resolve. This can include unlawful acts, such as arson. The phenomenon has been noted to affect civil servants, such as firefighters, nurses, police officers, and security guards.

'Hero syndrome' ex-firefighter convicted of murder in NY:

A young volunteer firefighter who prosecutors say wanted to be a hero was convicted Friday of murder for setting a fire that killed a mother and three of her children.

Experts Say 'Hero Syndrome' Not Common Among Police:

While there are no known scientific studies on ''hero syndrome'' crimes, experts say that police officers are involved in such crimes less often than firefighters and security guards. They also say that it is rare to find a case in which a bomb exploded, injuring the person who allegedly set it.

You could call someone who instigates a process that spirals out of control a Sorcerer's Apprentice.
In the poem by Goethe the Sorcerer's Apprentice casts a spell that gets out of control and he can't stop it, his attempts to stop it just make it worse.