How to keep my turkey burgers from crumbling
Ground turkey is usually very wet, I've found that breadcrumbs bind it together well without using egg. I prefer panko breadcrumbs for this, their large size seems to work better. 

Adding salsa isn't likely to help you much, the added liquid is going to make it hard to get it to stay together. If you want the flavor of salsa then try adding dry spices and tomato paste instead, those will absorb moisture rather than contribute it. I like a combination of paprika, cumin, and ground sage in my turkey burgers. 

Also, I've found that cooking the onions a bit before adding them to turkey burgers gives better result because it drives out some of the moisture and makes them a bit more tender in the cooked burger.