This is what I used to do and still do to some extent (DS is four now) - you say you counted down incrementally with him. He will have no concept of what "ten minutes" is let alone that it's longer than "two minutes" (And I bet you use the colloquialism "In a minute/I'll just be a minute" too to mean a short time probably longer than one minute - confusing when you think about it!) - basically, this is pointless as what you intend as a clear warning is total gobbledygook for him and being taken away from what he is playing with comes as a total shock. (Also has the annoying side effect that he eventually realises that "In X minutes" means "You're going to have to stop what you're doing at some random time quite soon" and leads to an instant tantrum!)
What would be better is counting the time in something that he understands, so you speak to him and tell him that you have to leave soon, and tell him where you are going next. If you like, emphasise some fun thing about what's happening next, riding in the car, seeing Daddy at home, having a snack, etc. Toddlers like to know what is happening, it helps them feel secure. Explain to him that he will have to hold hands, go in the pushchair, go in his car seat (whatever you usually have trouble with him agreeing to) when X happens. Sometimes just the prior warning is enough for them to agree without a fight.
Then give him a concrete marker for time that he will understand - for example, say he can push the train around the track three more times and then it is time to go. If he can't count very well yet, then count with him three times. But explain before he does the three times, that after those three times, it's time to get into the pushchair. You can work choice into it too if the choice is not overwhelming or you think it will be quick. So at the park, you could say it's nearly time to go home, you have time for one more thing. Slide or swings?
When that's over then (hopefully!) he understands that it's time and comes along without a fuss. If not, then you remind him that the train has gone round three times now, and it's time to go. Remove by carrying if necessary. You can validate his feelings and help him feel heard - say I know you feel sad. You wish you could stay and play with the trains. It would be fun if we could play with trains all day. It's okay to be sad about that. Just matter of factly, because remember that a tantrum is just him being overwhelmed by "big feelings" and he should come out of it, but I don't think it's wrong to strap them into a pushchair if you can't trust them to walk safely.
Some people believe that any kind of attention is wrong during a tantrum. Others don't. (I don't). However you'll get to know your own child and whether they're being helped by the attention or whether it winds them up more. Whatever you choose you'll have people who disagree so to an extent you have to pick your strategy and stick to it, ignoring any comments. People do like to comment on things that are none of their business, especially for some reason when you're a parent!