DSLstats compares the current values of total traffic reported by the modem with the previous values, and in normal circumstances the difference between the two sets of values is taken as the traffic during the period between the two readings. If there's a long gap between the readings, or there is something anomalous in the values, then an assessment is made and appropriate action taken to avoid reporting silly values. In your case DSLstats couldn't make sense of the values immediately after restarting the program, so it made the new values the new starting points, and added the 'implausible' comments to the event log.
As to the other issue, I suggest that you check the snapshots configuration, particularly the items to do with timing.