I could swear that this used to happen automatically. However, since I migrated to a new phone (now an HTC 10 running Android 7/Nougat - my old phone was a Galaxy S5 running 6/Marshmallow), I also have to open the app once to sync the tracking info from the website. Then tracking works as usual.
I tried disabling battery optimizations for Deliveries in case that was affecting things, but it doesn't seem to have made any difference. Anyone have some ideas on what we should try to resolve this?
Edit: for what it's worth, I'm using the google-account sign-in, not a Deliveries account. I'm also using the app's default settings (except for logging in), and I disabled the 'double back to exit' option. I could try making a Deliveries account if that might work better?