Mikado - another poster has mentioned this, but I think it is worth repeating:
The childminder called it a 'silly tantrum', which is very different to saying 'he was a silly boy, having a tantrum' - I have always believed it is a good thing to separate the bad behaviour from the child - ie. 'That's a naughty thing to do' rather than 'You are a naughty boy' - hate the sin and love the sinner, sort of thing.
It may actually be quite a positive approach, because it will help your son learn to differentiate himself from his behaviour, and that might help him learn to control his behaviour - something he is right at the beginning of learning.
I did have a slight chuckle when you mentioned 16-year-olds being able to control their behaviour and not have tantrums, though! I have three dses, aged 17, 19 and 21, and whilst the first two were relatively easy, in the teenage years, ds3 was an utter nightmare, and I despaired on a number of occasions, because he would have the most epic tantrums, over the most minor of things - but then I heard about a book called Divas and Doorslammers by Charlie Taylor, in which he says that, during adolescence, children's brains are actually changing, restructuring, and during that time they lose some of the abilities they previously had, around empathy and social behaviour - and this is why the teenage years can be so hard. Ds3 lost his ability to control his temper - there was plenty of diva behaviour and doorslamming, and I was called some very choice names.
One of the tantrums was because I refered to some arse-y behaviour on his part as him 'getting his head in a point' - something to which he took huge exception! That was definitely a silly tantrum!
They do grow out of it, once the restructuring of the brain has finished, and these lost abilities do return. Ds3 is now a reasonably acceptable social animal, is far more empathetic than he was a few years ago (when there were times I couldn't see us surviving until his 16th birthday), and the tantrums are largely a thing of the past - I do see the odd one start to bubble up, but he can control it now.