You say it runs an hour or two after it "should" be finished. Have you verified that you're actually waiting long enough for the process to end and for the unique "term 2" to be logged? (It's also remotely possible that something odd is happening with timezones, but that's just speculation.) Another point--as your search is written, you're not distinguishing between which terms you find. If you happen to find two term 1s in the daily log and no term 2s, then your search will return those times. You should be sure the events are unique and that term 2 will always follow term 1 (and that it completes on the same day), or else you will need to make your search more specific.
If you're sure the event is being logged before the search is run, then it might be that timechart is doing something funky with the time bucketing. I would try this instead:
"term 1" OR "term 2" source="logfile.log" | eval time=strftime(_time,"%r") | eval date=strftime(_time, "%D") | stats earliest(time) as start_time, latest(time) as end_time by date table date,start_time,end_time
