Allow for freedom. Designers flourish with freedom of expression. Explore their portfolio and make a decision based upon the idea that their artistic expression can move you vision forward.
Believe in them to create the experience you desire.
Obviously, their portfolio of past work is the best start. Although a designer can adapt their style to meet the needs of each client, you should see a design identity across the realm of their work. Does their past work *look like* the kind of work you are looking for in your brand identity?
A logo and an app icon are *very* different things. From a process perspective, if they suggest designing both the logo and the icon at the same time, they are inexperienced and should be avoided. A good designer should first want to iterate the logo in black & white without text. Once the logo, typeface and colors have been locked, then an app icon can be designed that is pixel-perfect.
I would suggest looking through Dribble to find someone with a great portfolio that includes app icons.
Happy to talk through this in a call if you need more clarity.