The discrepancy you will see is due to the rate limits we introduce in the way the system communicates. When on local mode, you will get updates up to every 15 seconds as the energy monitor transmits its information. However, we limit the data sent to the server depending on the current/total values in an effort to reduce unnecessary repeating data. This can result in the readings on the server being relatively out of date, but the values will be slight. Your "live" current use will be within 10% of the value shown when away, and the total use will be within 0.1kWh.
The total yesterday use will be the highest the total use yesterday reached when passed to the server. Similar to the previous paragraph, it is possible that it may be slightly out of sync, but the discrepancy will be very slight in this instance.