Who defines the conversion-values values? How is it determined which value will be sent back?

You as the advertiser define the conversion values and to which events they correspond. Branch allows you to map your Branch events to conversion values via the Branch dashboard.

Note that the Apple App Store client on the device determines which conversion value gets sent back on the postback based on its own logic: only the highest value that is accepted before the SKAdNetwork timer expires will be provided in the postback, and only if it passes Apple's secret privacy thresholds.