The first thing you must accept is that threading is hard.
A "program using threading" is about as generic as a "program using memory", and your question is similar to "how do I not corrupt memory in a program using memory?"
The way you handle threading problem is to restrict how you use threads and the behavior of the threads.
If your threading system is a bunch of small operations composed into a data flow network, with an implicit guarantee that if an operation is too big it is broken down into smaller operations and/or does checkpoints with the system, then shutting down looks very different than if you have a thread that loads an external DLL that then runs it for somewhere from 1 second to 10 hours to infinite length.
Like most things in C++, solving your problem is going to be about ownership, control and (at a last resort) hacks.
Like data in C++, every thread should be owned. The owner of a thread should have significant control over that thread, and be able to tell it that the application is shutting down. The shut down mechanism should be robust and tested, and ideally connected to other mechanisms (like early-abort of speculative tasks).
The fact you are calling exit(0) is a bad sign. It implies your main thread of execution doesn't have a clean shutdown path. Start there; the interrupt handler should signal the main thread that shutdown should begin, and then your main thread should shut down gracefully. All stack frames should unwind, data should be cleaned up, etc.
Then the same kind of logic that permits that clean and fast shutdown should also be applied to your threaded off code.
Anyone telling you it is as simple as a condition variable/atomic boolean and polling is selling you a bill of goods. That will only work in simple cases if you are lucky, and determining if it works reliably is going to be quite hard.