Learn Spanish (Latin America): Él explicó que ya no ejercía, porque montaba un negocio nuevo. - He explained that he was no longer practicing, because he was setting up a new business.

This is exactly how tense backshifting works in reported speech! The original speaker likely used the present tense for his direct quote: "I no longer practice (ya no ejerzo) because I am setting up (monto) a new business." Because the reporting verb is in the past (explicó), those present-tense verbs shift "back" a step in time to the imperfect tense (ejercía, montaba).

Why does the translation say "practicing"? Doesn't ejercer mean "to exercise"?

It can mean to exercise a right or authority, but when used on its own regarding a career, ejercer means "to practice a profession" (commonly said of doctors, lawyers, or architects). If you want to talk about "exercising" for physical fitness, you should use hacer ejercicio or entrenar.

I learned that montar means "to ride." Why is it used with a business here?

While montar does mean "to ride" (like a horse or a bike), it also commonly means "to assemble," "to put together," or "to set up." Montar un negocio is a very natural, everyday Spanish phrase for "to set up a business" or "to start a company."

Just as a refresher, what is the exact difference between ya no and todavía no?