Keep in mind that I am flexion intolerant with a past history of lower back issues. Fortunately I'm pain free for years now. I've wrote about this a lot on this forum. I just state this because I am probably much more aware of my lower back position, AND, much more sensitize to tightness, than the average person swinging bells. I'm stopping even with the slightest indication of something being wrong.
If I feel that extreme tightness, I like to do the cobra pose (yoga) on the floor or even on the bed. I learned this from Pavel in his book (Super Joints I think). I'll bring a book and stay in that position for up to 30 min sometimes. This doesnt happen to me very often anymore, maybe twice per year. But it happened over the late December Holidays at my parents house. I was on 2 week vacation in Florida and I brought a 32kg bell (relatively light bell for me), and went to do my 20 repeats of 5 snatches. Half way through, my back tightened up. I stopped and did my cobra and was fine. 2 days later I was back to normal.
The 1st thing is to get your form checked. And you did this and this, in general, doesnt seem to be the issue (unless it breaks down under fatigue, which the trainer may not have seen). I dont know anything about you or what program you are doing, or what sports you are into (based on your pic some martial art, which may also strain the lower back?). But, in general, I would CONSIDER doing less. Especially if you think it is happening later in your workouts. Pareto's Law, the 80/20 Rule, states you can likely get 80% of the benefit doing 20% of the effort. For example, if you were doing 10x10 3 times per week, temporarily try 10x5 or 5x10 3-5 times per week. Just try it and see if your back tightness goes away. You are still likely getting 90% of the benefits of your swings, even by doing less.