Push notifications for routine start reminders should work with or without the upgrade, but they don't make it through 100% of the time because of network imperfections. They are generally reliable, though. You can tap the [•••] button on the Activity list screen for your routines to see if the notifications are turned on. Also you'll want to make sure your app has the permissions to receive notifications in your device's settings.
Notifications are usually sent about 5 minutes before a scheduled start time and will make a distinctive chime sound.
Please send me screen captures if you're still having problems getting it to work and we'll see what we can do to help.