The main reason for a higher cost was that I had my assets stored in an additional bucket that I've created aside of the default one. As it turns out when you're utilizing additional buckets the different pricing schema is applied. Brief information in this regards can be found in Firebase pricing page under ? icon corresponding to Firebase Storage entry.
This is the estimated pricing for common usage. Firebase Storage free
limits are enforced daily and refreshed at midnight Pacific Time. In
the Blaze plan, fees for Firebase Storage are based on usage volume.
Firebase Storage usage fees are processed as Google Cloud App Engine
usage fees for the default bucket, and Google Cloud Storage usage fees
for any additional buckets. For more information, see pricing for
Google Cloud App Engine and Storage.
Additionally, prior to my current implementation of assets cloud fetching, I had it done via publicly accessible HTTP protocol (there are many Youtube clips which "teach" this approach). I'm not quite sure but that might've had an impact on a pricing schema as well (it's a little bit too convoluted reading Google's documentation in this regards and understanding all the terminology). On top of that this approach presented security threat as the urls were publicly accessible to anyone - in order to prevent it one should always think of some kind of authorization mechanism.