The 6 saves a day got nothing to do with the logic here. But it means, that with relative many saves, you are able to investigate what might have happen, if someone is interested. I can just say, that these values did change by 2 point increase and at the same days as I had made a note, that a training with Jennifer took place. And I have, as you, also most the times seen, that nothing happens with this display value when Jennifer give you the two points.
Sorry about the day-term - it has been my personal way to record what day something happen. Day 1 is the Saturday when MC arrive to island. So the day 9 to 10 is the second Sunday to Monday transition in game. At this transition you got no reset to zero when you got something level up, but a reduction of the needed level up value. It do not think, that it matter much, but it just puzzled me when I tried to analyze how these things work. The developers most likely had got a good reason for doing it like this.