Are you saying that you remind him of the schedule during the day and that you give him 5, 2, and then 1 minute warnings and then add counting to three to those. I think that is over doing it. Do one or the other and leave out the detailed plan for him. If you choose the counting, count to 10 slowly. Three seconds is not enough time to transition and do most things. I think at 3 he will not be able to respond to the multiple warnings.
You can do both techniques but not both at the same time. Some tasks need a warning ahead of time. An example would be: "We're leaving for the store in 10 minutes." This makes him aware that there will be a change. Then when it's time to go tell him to get his coat and start counting as you head for the door if he doesn't head for the coat. Most 3 year olds don't benefit from a warning that requires action later because they will be distracted during that 5 minutes. In this instance the warning is only for transition purposes.
If the purpose of a warning is to get him moving and he doesn't start moving then start the countdown but don't wait 5 minutes. He'll be distracted in that 5 minutes. To warn several times does tell him it's not time to do it yet.
I try to time my counting so that the child is able to get it done. Therefore I may count to 15 one time and 5 the next. I don't think I ever count less than 5. If they are moving towards getting it done I pause towards the end to give them time. If they're not headed in the right direction I tell them to step on it in a humorous way. For example I might say, "oh,oh Johnny is just too slow today. Guess he needs a push. And then I'd rush towards him with my hands out. Usually that would cause him to get it done. But if it doesn't or if he's developing a pattern of not cooperating I'd provide a consequence based as close as possible on what he was or wasn't doing. If it's picking up toys then I'd pick up the toys and put them away. I would let him know that is what would happen.
The goal is to get the toys picked up. The counting is just one way to get that done. At 3 he will need some time to switch from what he's doing to picking up the toys. Giving him a 5 minute warning doesn't get him started on picking up the toys. It does help him know what's coming. He won't start picking up until you start counting. A warning is just that a warning and not a call to action. At 3 he'll most likely have forgotten that you gave him a warning. Tell him to do it, wait a few seconds and then start counting.
You wouldn't have to count if he's steadily doing what he's supposed to do. In fact counting works best when it's not used all of the time; if it's used only when he needs an added incentive.
Another technique that I use instead of counting that is similar is to say," I bet I can get to the door before you can." Kids love competition. My 6 year old grandson now tells me he can get to the car before I can and if I'm lagging too far behind he tells me to please hurry up or run, Gramma, run. :):)
Telling him the schedul isn't effective in getting things done either. At 3 he can't remember the schedule. Tell him what the next thing will be before the last thing is done. Or you can say, we're going to the gym today but telling him each step has no meaning for him. When it's getting to be time to leave tell him that as soon as he picks up his toys you're going to the gym. You can also use going to the gym as an incentive to get other things done. You can say we need to get things done so that we can go to the gym later. Then, if he balks about doing something you can tell him that you need him to do this so that you'll have time to go to the gym. Deal with one activity at a time. At 3 the most he can remember is one thing at a time with a transition in between activities. The length of time he needs for a transition depends on his personality.
I wonder if you're trying too hard to do the best possible job. Try relaxing and not worrying about whether or not your son understands how the day will be. Have in mind what you want to accomplish and you arrange activities so that you can get it done but he's too young to be involved in the plans. You're the mommy. You're in charge. As long as you are reasonable in what you expect from him he doesn't need to know the details to accomplish one task at a time. It's too much information.
I found this hard to explain. Perhaps I didn't understand what you were describing. Hopefully, you're not giving him multiple chances but if you are he is immature and will take those chances. One thing at a time all day long sounds boring but it's not to a small child. It's Mom who needs to know each step.