This isn't out of the realm of normal toddler behavior, but it seems to be true (from experience, and the anecdotes of other parents) that for some young children, mobile games, cartoons and other screen time is so over stimulating to their brains that they become quite out of balance and show personality changes like hyperactivity, increased tantrums, aggression, and sleep disruptions. There is some scientific basis to the idea that these are more than behavior problems, but have something to do with screens causing intense brain and limbic stimulation, which is a potent combination of low-level stress and strong pleasure/reward. For susceptible kids, it can be almost like an addiction.
If you think this is what is going on, and you can't correct the situation by simply limiting screen time and engaging him in more imaginative play, outdoor play, interaction with other people, etc, you may want to consider asking your son's pediatrician for advice.
But I think that your son's case is a lot less severe than that. You say "I'm not strict but his mom is strict" and "He won’t listen to me... In comparison he is quick to listen to his mom". I think that one big part of the puzzle is that he knows he can get away with not listening to you and keep playing on his device. He probably has a good idea how many times he can tell you to wait or ignore you before you get serious about the idea of taking his ipad.
You can handle this the same way as any other common childhood behavior problem: positive reinforcement (praise, nice things happen) when he listens to you the first time, and negative consequences when he rudely ignores you. Remember that punishment, especially overly harsh punishment, is usually less effective than rewarding success. Give your child plenty of chances to succeed, and don't 'set him up to fail' by always interrupting his games just to see if he reacts, but once a warning is issued (i.e. "get your shoes on now, or you will lose your ipad time for tonight"), and he ignores or disobeys it, you must follow through, every time, without fail.
Ideally, start with notifying him of the upcoming transition so he has time to process the instruction and wrap up what he's working on, ("In five minutes it will be time to wash up for dinner"), then once the five minutes are up give an instruction ("Please put the game down and wash up now."). If he does so, thank him for listening and express that he did a good job! If not, give a warning, ("Wash up for dinner now, please, or you will lose your tablet time tonight"). Then, thank him if he listens, and if he doesn't, let him know that he's subject to the consequences ("You chose not to listen when I asked you to wash up for dinner, so you can't have tablet time tonight.")
Also, I recommend that you limit your son's screen time, at the very least temporarily, to see how that impacts his health and behavior. He will certainly protest that it's unfair that his cousins have unlimited games and cartoons, but life isn't fair, and while you are right that you can't tell another's child not to do something because yours is getting spoiled, you also can't really be permissive to the point of being detrimental to your child's wellbeing just because other children can handle screen time better or their parents have different rules.