Have not heard of the LEDs staying on after turning them off. Staying on sounds like a different problem than most with LEDs. If you want to do minor troubleshooting before paying the trip charge for your warranty work, here's some ideas. Although, being the first year, hopefully they do the work completely for free.
I'll bet the problem is isolated to the same side of the tub? Check out these photos from inside my 740. I am sure your tub is similar.
https://www.whatsthebest-hottub.com/forum/index.php/topic,17965.msg185113.html#msg185113Looking at it, you should see a blue bar with wires in it. That is the box that distributes the power to the LEDs. You can see how it plugs into the main box. You could cut the power to the tub (for super safety) and swap where those boxes plug into the main board. If the problem moves, it is the main board. If not (or if you only have one blue box thing), it could be the blue box for that side. You could start unplugging things and plugging some of them from the other side in just to see. That is a bunch of work to find out you still need a tech to come out for the warranty work.
Sadly, it looks to me like the LEDs are a standard problem now with Jacuzzi. Search the forum, you are not alone.
I have replaced all cupholders, both waterfalls (twice) and one headrest (LED was fine, but plastic broke). Only the cupholders and first set of waterfalls were under warranty. The second set of waterfalls went just after the first year of ownership and way less than a year after replacing - no help from dealer nor Jacuzzi. We went months with the waterfall LEDs unpluged because they'd short the entire system out and we'd have not lighting. At $200 a piece just for the part, I was not in the mood to pay $400 for some LEDs. I considered making something myself with some Christmas lights and college, but never did get around to it.
Hopefully I am not jinxing everything by saying they have been working now since late January.
I do believe the cupholders went because they were over-tightened during construction and cracked, allowing water to slowly get in. You could tell from looking in there. The waterfalls were just poor construction of the LEDs. The first set of replacements went relatively quick and you could tell from looking at them, water got in bad. I found replacements online for around $88 each instead of the $200 each. Before I installed them, I coated the seam in the plastic with Boss 802 (maybe 801) sealant. They *seem* to be holding up pretty well. They've lasted longer than any other set I've had!
https://www.whatsthebest-hottub.com/forum/index.php/topic,19103.msg192940.htmlhttps://www.whatsthebest-hottub.com/forum/index.php/topic,17960.msg185059.htmlhttps://www.whatsthebest-hottub.com/forum/index.php/topic,20557.0.html