We recommend installing your VPN client on both your laptop and mobile device. There are differences in running a VPN from the endpoint (your laptop, in this case) and the device that provides your internet access (your Android phone, in your case). The primary reason that we recommend both is that you’ll likely want to be able to use your VPN independently on both devices.
The VPN creates an encrypted tunnel from your device (either or both) to the VPN server that you’ll appear to be coming from on the internet. Creating that tunnel on your mobile device will protect activity from your mobile device directly and your tethered laptop. However, if you can’t use your mobile device to tether from for any reason (poor service in a particular area, service is down, data plan limitations, etc.), being able to create that tunnel directly from your laptop is a nice option to have. This gives you a lot of security and privacy protection if you need to connect to the internet via other unknown and untrusted networks.
You won’t necessarily need to turn on the VPN from your laptop if you’re tethered through your mobile device and your mobile device is using a VPN, but in doing so, there is an added layer of protection. You can essentially tunnel an encrypted VPN connection (via your laptop) through an existing encrypted VPN tunnel (your mobile device). You can choose to have your mobile device come out on one location on the internet and your laptop from another. Keep in mind that stacking VPNs like this can contribute to performance issues.