When a MySQL process is first created (or started) it can be very resource intensive. After things settle down, our system can very carefully start to prune away at bits that aren't being used to get the resource usage down. This process is very conservative so as not to impact performance, and it can take a couple of weeks.
The effect of this is that the initial billing estimates of MySQL are based on a usage level that isn't (usually) sustained, so it's not unusual for it to report that a new process may cost several dollars a month because based on that limited sample, it would. But as things settle down, the estimate will typically go down to reflect your real usage. As of September 2016, the median cost for MariaDB 10 processes is about $0.60 for resources and storage combined and over 72% of MariaDB 10 processes cost less than $1.00/month.
If your usage records and estimates remain high for more than a week or two, you may wish to review your usage to see if something is more intensive than you expected. Missing indexes, for example, can really increase the resource usage of a MySQL process.