A few things come to mind, first is what fluid did they use in the gearbox? Second, what condition is the battery in? If the battery is not holding its charge that well, it can cause spurious faults on the gearbox ECU and other ECUs as well. The clue here is that it happens after a cold start, when there has been the most load on the battery to start it. By the time you've started it for the third time in the day, the battery would (or at least should) have enough charge to cope with a warm start without dropping the voltage enough to cause a spurious fault.
As you might guess, my thoughts are directed at the battery being at fault here!
Recently on my S Type, i hadn't used it for about 3 weeks and when i started, it came up with "Auto Gearbox Fault". I ignored it for a few miles, then hit the clear button and it went off and stayed off - hasn't returned since so i'm assuming that it was just a low battery. Sometimes it will also try and tell me a tail or brake lamp (sometimes both on both sides!) have failed as well if i haven't used it for a couple of weeks.