Yes Azamax is made from neem. It is hot pressed neem oil I think, which actually degrades the neem. I have used a lot of stuff and tbh the stuff that works the best is Neem Oil.
A surprise to me was when I used Mighty Wash on a plant that was finishing with bugs on it. My buddy at the grow store told me to use Mighty Wash because it was safe up to the day of harvest. I did just that and it washed off everything. Bugs, webs, a few mildew spots. I let it dry and harvested 3 days later and everything was still clean. This is my new choice when I am getting close to harvest. You can't spray neem within 2-3 weeks of harvest because it can impart a bitter taste and smell to your herb. If you have used it before, you know what it smells like... Garlic and Ass Jam. I wouldn't like it either if I were a bug. I hate getting it on my hands, let alone being covered by it.
Be sure to use a surfactant or wetting agent with it. You can go buy a normal surfactant at a grow store, or be smart and just get some normal antibacterial dish soap as a substitute. Any dishsoap will do, I just like the antibacterial ones. It makes me feel like the plant is cleaner, it doesn't hurt the plant at all, and it works great.
Ultimately, if you spray enough times with Azamax, Neem, Garlic, whatever, you will get your problems under control. Most people just don't want to take the time to properly spray down their plants. I have friends that have tried Neem without success, and I always ask them if they spray every 2-3 days and if they completely drench the plant. They never have done it right, and come watch me go to town and say that it is too much work, lol. I would much rather do it right and get it done, than dick with it for 3 months fretting about it and trying to vacuum off the mass of webs and mites. I have had an outbreak happen and after one proper spraying, the problem was fixed. I sprayed again like I was supposed to to kill of any eggs every 3 days, but after the first treatment I couldn't find anything under the fan leaves.
The great thing about Neem oil also is that it cover SO many different problems. I use it for Mildew and Mite prevention, which most of us do. The Mighty Midwest Mildew is a sonuvabitch. It will pretty much do away with any insect( even beneficials,) it is a fungistat vs Powdery Mildew, Bud Mold, etc. Basically it is everything that I need in one really cheap bottle.
I use 1oz of Neem Oil, 1/3 tsp of Dawn Antibacterial Dishsoap per gallon of water. Do not try to be cute and help the Neem stay emulsified in the water by using hot water. Hot water kills off some of the beneficials in the Neem Oil. This is why the Hot press neem products such as Azamax do not work as well as Cold Pressed neem oil. Note, I said "as well." I can never kill off everything with Azamax, I just find it to be not as effective as Neem Oil and it takes longer.
If you can deal with the smell for a couple weeks and want to do it properly, I would use the neem. After everything is under control, I normally use it ever 2-4 weeks if I get busy and don't have problems until a Sativa enters the room and I get a 101st Airborne combat drop of a million mites that find my sativas even though nothing else in the room is showing problems.