Hiya,
I feel like I've opened a can of worms so my apologies. I didnt mean to burst the excitement bubble, the watch is stunning!!
It could be as
srhoque said that the machine wasn't calibrated correctly resulting in an inaccurate reading or it could be dirt/dust or it could be a faulty movement, we just don't know unfortunately.
My understanding, and others will correct me if I'm wrong, is that for the most part, TDs act as middlemen/women, and will send QC pictures for the buyers approval of the watches they receive from the factory.
If the buyer rejects, for a valid reason, they send back to the factory and get a new one. I know that some TDs have watchsmiths that can do minor fixes, but for the most part, I believe they just act as a go between between us and the factory.
But back to the 13s/day, even if it was accurate, that's about 90 seconds per week, or 6 minutes per month.
Even if it was your only watch, and you were wearing it 24/7, or when not wearing it, it was going to be on a winder, then you'd notice.
But would ~6 minutes a month really bother you? Only you can answer that as your money at the end of the day. For me, it wouldn't, but I rotate my watches weekly, and generally have to wind them anyway, so never really notice or bother with lost/gained time.
If you're visually happy with the watch, I wouldn' reject it, but ultimately your call.
Hopefully your TD can give you some additional assurances.
Best of luck