the myChevy app is linked with the OnStar Guardian app so unfortunately, yes, you have to pay a monthly fee to have remote vehicle functions from your smartphone. If you download the app when you first purchased the vehicle, then you'll have full access to the app's features during your OnStar trial subscription period. I ended up buying the remote start key fob from the Chevrolet accessories website and took it to a dealer to install for me (you can do this yourself at home with the same instructions provided by GM to the dealers, but you'll need a more advanced OBDII scanner with the capability to make edits to the vehicles programming. Wasn't worth the cost justification in my case, but maybe it is for you.). The remote start on the physical key fob is independent of the myChevy/ONstar app and will work up to a certain proximity away from the vehicle. The only real benefit I can see to having the myChevy app remote start over the button on the key fob is if you want the ability to start the vehicle when you are well outside the range of the key fob or if you have large obstructions between your vehicle and key fob (e.g. concrete walls).
I'm still within my trial period for OnStar services and I honestly don't care much for the remote start from the myChevy app mainly because it seems to be inconsistent with sending the command to my vehicle.