Ah, that's probably why we usually add the coffee when water is done boiling. Then bring it to a boil one more time. Or up to four times, depending on taste.
shrug Still won't take 10 minutes even if you're boiling slowly at low heat. Unless you're making a super large pot, but making more than two turkish coffees at once is far out. 2 is the number you shall make.
Your description sounds a little different than how we make it. Guess the recipe changed in the ~1000km journey up to us.