Even coming from New York, with all its flight options to Europe, it can be hard to make a 3 PM arrival into Palermo (the airport is about 35 to 45 minutes from the city center, for one thing). But in addition, if there's one thing EVERYONE who has taken a tour (RS or anyone else) emphasizes, it's that you should plan to arrive at least one day before the tour start.
You could fly into another European city the day before, then take a flight to Palermo that morning. If you're going to do that, Rome is the best choice, simply because it has multiple flights on multiple airlines each day to Palermo, so you'll have the most options if something happens. If you, instead, use a city with 1 or 2 flights a day to Palermo, and the morning flight is canceled, you'll miss the start of your tour.