Starting school (kindergarten) was really hard for us with my son, who is very smart, gifted, but also very strong-willed, and very active. If you think about it, starting school is REALLY HARD, especially for boys. Suddenly, they are expected to sit still, follow rules, not play too rough, not speak out of turn, color, cut & paste, have good handwriting, etc. It's really hard! Our son doesn't have ADD, but he does have an explosive temper that he's learning to control. If you think your grandson has ADD, then seek and get a diagnosis. Don't self diagnose, and potentially label him with a condition unnecessarily, especially if you're not willing to medicate or treat the condition, if that's what it is. I think there are things you can do proactively to manage YOUR grandson's response to certain situations, if this is just a maturity issue and not a medical issue.
A few books that were helpful for us were by Ross Greene, a counselor who specializes in a technique called "collaborative problem solving". "Lost at School" and "the Explosive Child" were the ones I read, along with "how to talk so your kids will listen and listen so kids will talk". The things I learned were first, kids try to do their best and explode in tantrums because they can't emotionally cope with circumstances. To help them through this, they need to develop some tools to manage their response in the immediate crisis, and then figure out a separate coping mechanism strategy for the adults in their lives.
In my experience, quick consequences often escalated the situation & made it worse. And I really needed to manage MY response - try to avoid getting frustrated, take a deep breath, have patience, compassion, but still take charge. Talking about my son's tantrums separate from the incident allowed us to figure out a collaborative solution calmly. Some of our strategies include simply acknowledging my son's feelings, and letting my son take a break. Example: "I see you are very upset that you can't stay at the playground. I wish we could stay but we have to go home for dinner. Please take 2 minutes to quiet your thoughts before we go home. At that time, I expect you to come to the car with no fussing." Even separating himself for a few minutes to breathe deeply and be angry helps him calm down despite the disappointment! I'm sometimes shocked at how well it works. Then separately from the incident, talk about what happened. "I like going to the park after school, but I worry that if we go, you won't want to leave, and we'll miss dinner. What can we do to solve this?" Let him help come up with a mutually agreeable plan, remind him of that plan before you get into the incident, and then execute the plan.
The more he gets used to a pattern of successful solutions & strategies and managing his response, the easier it will be.
Good luck!
I would also add that my son is now in 2nd grade and although he's still strong-willed, actual tantrums are now pretty rare. His routine is pretty consistent, and when we think there's a risk of a meltdown, we talk about it ahead of time, and try to invoke some of the coping strategies as a solution. Not only has he grown up and has more emotional maturity, but he's also got a better set of behavioral tools to calm him down and work through any particular situation.