This is the reply I received from the CNET Download product manager and I hope it clarifies the count:

The "Last week" download count is the number of downloads from the
*previous* week, so if you downloaded the app on Monday and checked back on Tuesday, that count would not update as it's still showing downloads from the prior week.

The total downloads count does update every night, so that's the one you should track.

Let me know if this makes sense.

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