Typically when you use an "auto" route, the software or execution server picks the route to use based on current market conditions and the specifics of your order. If a route is used that supports stops internally, usually you can walk away from your computer with the comfort of knowing your stop will be managed by the destination. In some cases, on some trading platforms, they hold the stop orders client side so you need your application up and running in order to receive the market data to trigger the stop order.
It really just depends on the trading app and the route used. I suggest you speak to your broker that provided the product and get a definitive answer.
If you're looking for a new broker with better customer service or more products to choose from, consider ProTradeFinancial.com. I hope this helped you a bit.