I find it admirable although a bit concerning that there's transparency with the financial metrics. Most employees don't need to know that information, both for the company's sake and for theirs.
That information can affect the employees as they will be making plans:
- if the metrics look bad then they will make plans to jump ship, productivity will drop, word will spread or they will simply worry when it's not their job to worry about financials.
- if the metrics look good then they can expect some pay raises or benefits or improvements which might or might not be in the future plans of the company.
The company being a startup can be affected if the information leaks out. Possible investors might back out or propose some outrageous things or the competition will see inside the company also and they will be "data driving" on your back.
Financial information should be on a need to know basis.
Now back to the issue at hand about "data driven". From my experience, this means that the company will aggregate all kinds of events and data (financial, user, metrics, feedback, everything). Some of it will be for vanity (like app downloads) and some will be actionable (like where did the app downloads come from which allows you do double down on a good source).
The purpose of the "data driven" company is continuous improvement through data. Observe data, propose changes based on data, experiment (A/B testing at the minimum), observe results and carry on the cycle. For example: the UI of the application, the UX, the features offered or the price points for the features. Everything should be registered, tested and improved upon.
You said something related to engineering tickets being related to app downloads. That is a pretty huge conjecture there but if the data shows this then it must be true (!Warning: correlation does not imply causation). Recording the trend and velocity of the engineering tickets is a good metric that can be actioned upon later on. Usually the 5 why are applied to determine possible relations between events and getting to the core issue of something so you can do actions and tweaks on it (why has the number of tickets increased/decreased? etc.).
As for the monthly data/metrics talk: the "data driven" company is based on a constant 24/7 talk about the metrics and how to act upon them.
Also as for making the data requests public, the same as for the financial metrics apply (need to know basis or some kind of marketing point).