Knoddy is right on all counts. I've jihaded Constantinople before while it's 0% Islamic. There were definitely non-capital targets and secret resource thing also isn't the case.

Just keep up your warmongering and right before you capture a city, see if you can call a jihad on it. If so, join the jihad and hire up some cheapo Jihadi units. BTW, don't forget to stick every eligible army you have into the jihad. It makes them free upkeep (if only for a turn), allows hiring of cheapo jihad units everywhere, and also gets the generals good traits and troops experience when they succeed.