Thanks for your answer!
The problem is not the connection between OBD reader and smartphone, this functions very well.
When the motor is running, so the lights should be off. But for example the ABS light is on. So i think it must be a problem with the protocol between car and OBD reader.
I would suggest you to connect the OBDLink app with the reader with the ignition ON, engine OFF, and read the "diagnostics" section for any DTC errors related to your findings. It is definitely not normal for dashboard lights to remain ON after the engine starts, so doing the above can be a good starting point.
As for the OBDLink OBDII connection protocol, I have it set on AUTO. This is probably not related to your issue, but it won't hurt to check that your vehicle model is properly selected in the configuration menu and you download the latest enhanced OEM add-os for Mazda vehicles.