From Google Play

Used primarily for Parent devices and Android tablet devices. Parents that have kids with smartphones and want to monitor calls and text messages need to use the version from our Website (steps below). 

On a child device, the version on Google Play will not automatically update as Boomerang Parental Control is a background service. The user (child or parent) needs to manually forceBoomerang Parental Control to update via the Google Play app. Follow these steps: 

1. Open Google Play
2. Tap Menu   My apps & games.
3. Tap on Update beside Boomerang Parental Control.

From our Website

The version available on our website is for parents looking to have our Call and Text Message safety features which cannot be provided via Google Play any more. The easiest way to update your child's device is to follow the steps here: 

1. Open Boomerang Parental Control on your child's device
2. Tap three dots in top right  About
3. Tap on Version xx.xx-sideload (or it could be Version xx.xx-gp). 
4. Our website will open > Tap Download
5. Accept the warnings and the app will update

Related

How to get Boomerang's Call and SMS features

How to install Boomerang on an Android device