Does Part 135 duty time begin at the start of a part 91 owner flight which occurred immediately before?
Absolutely, 135.267 (d) requires you to have 10 hours of rest within the 24 hour period preceding the completion of every 135 flight, and if the 91 flight is for the same company then it is not considered rest. Duty time starts when you are required to do anything for the company, and for a typical flight it starts when you arrive at the airport.  

For more information on rest, see this question and answer.