I downloaded and installed the app. from the Play Store onto my phone on 20 September. Prior to this, I had launched Seabreeze through Chrome.
My data usage pattern changed dramatically - see the graph.
I uninstalled the app. on 29 September.
It seems that every time I launched Seabreeze through the app, some 0.20GB of data was downloaded. If I launch Seabreeze through Chrome, the data count goes up by 0.01GB.
My phone is quite old, namely a Samsung Galaxy S4, running Version 5.0.1 (aka Lollipop) as the operating system. The age may be contributing to the problem.
Has anyone else had similar experience with the app?

I would be really surprised if the Seabreeze App is the cause. It only transfers a small amount of data (and the graphs are rendered on the phone), it should use less than the Chrome version does.
To find out if it is Seabreeze, you'd need to go to the "App Info" on your phone, and look at the data usage - Android measures the data usage of every App, and it should clearly display it there.
Goto:
Settings -> Apps -> Seabreeze and then view "Mobile Data". On my Samsung, I can tap on "Mobile Data", and view usage by the month...
Or:
Goto:
Settings -> Data Usage -> Wifi (or Mobile) -> and view the graph -- scroll down and it will show which apps used what...