I also use JLC (including SMT and THT assembly services) and never had issues with them. The only thing "added" is the tracker number, which, if I don't mind placed randomly, I leave it as is, or I just place a marker (as instructed) somewhere where it does not bother me and they place it there.
You also have to check if you are within the specified limits for clearances! The automatic tests may not catch a violation or two and that may cause the "shorts". Full flying probe test option (which is for free, as far as I see) should help.
Even if all fails and you have a faulty board, contact them and report a quality issue, I'm almost 100% sure they will help you solve it (by issuing new boards). I had the experience in contacting them with some silly questions (some questions for very small boards assembly way under their minimum limits) and they did replied promptly and on subject. They really tried to help me, even if I didn't ordered anything yet for that particular case.
JLC is quite big and they don't mock around, if they did, then they would be out of business in no time. But they are not the best on the market, there are some way better, with better or more advanced services offered. But for the price, I would not complain too much.
I'm not advertising for them, this is just my experience with them...