I bought an upgrade today for my iPhone version. However, despite logging into the Android version on my tablet, the upgrade does not seem to have transferred over. Should it?
The upgrade you did is valid for your account, whatever device you use - Android or iOS and also if you use several devices.
You need to use the same account (user name or email address) which you did upgrade (in the Settings of the app) and then update cards (top right button of the app).