The reader used a synodic period of 29 days 12 hours and 44 minutes which is 29.530556 days which is slightly different than the 29.5305882 days of the true synodic month ( 29 days, 12 hours, 44 minutes 2.8 seconds) but this difference should not of itself contribute to the up to 2 hour ( 0.08 day) difference the reader reported between predicted and actual lunar phase. If the reader estimated the lunar phase times by eye, then such errors, and even larger ones, seem entirely reasonable and expected. One possibility is the time zone conversion. All phase calculations are based on exact time not on time zone. If you have the phase rendered in Universal Time and do the calculations, you should get the synodic period exactly. But for local time, you have to convert from UT of the forecast, to your actual local time by correcting for your longitude relative to Greenwich...NOT just correcting for your time zone difference. This latter conversion could easily give you errors in forecasting of an hour or so.
That's my best answer.