Does my ticket become valid at 09:30 (when off peak starts) at *my* station of origin, or does it only become valid on the first train it would have become possible to catch allowing for an 09:30 start from the origin shown on the ticket?
Unfortunately, many of the Railway's regulations, conditions and restrictions are poorly worded, and lead to ambiguity, uncertainty, confusion and in some cases, contradictions. You are quite right to ask for clarification in this set of circumstances.
I'll guess that the original intention when drafting this particular ambiguity was to treat the train you're intending to catch as a 'peak' train. Presumably you've had the same thought yourself, which has led you to ask. But if that guess is correct, the actual restriction doesn't say so.
I'm inclined to agree with
richw,
bb21 and
PermitToTravel that your use of the Off-Peak ticket starting short and starting after 9:30 is, technically, permissable. But I must caution you to be prepared for a challenge. Some people, quite understandably, will take the opposite interpretation. On some routes in particular, a more 'robust' approach to enforcement is taken, and consequently, I advise you only to use that ticket in such areas if you are willing to risk a few minutes delay while you are questioned, and the possibility of follow-up correspondence to reach an agreement.
Or in other words, my advice turns not of the precise wording of the restriction, but on your willingness to participate in a discussion, a discussion which will be as constructive or as confrontational as you and the other party chose at the moment of ticket inspection.
Again, I don't disagree with bb21 in asserting that it is not for you, the passenger, to provide the evidence that you boarded after that 9:30 threshold, but if you are travelling in one of the areas where enforcement is 'robust', then I will echo the advice of others that those who choose to be 'creative' in their travel in order to pay less for it, then they should be content to be questioned about it, and consider whether it might make for a better day to have some sort of evidence to demonstrate compliance with those ambiguous conditions.