Yes they do I believe. I had trouble with my daughter and time outs around same age too - think they aren't as helpful past six.
In general, I'd suggest a mixture of carrot and stick, and aiming for "calm assertive" (easier said than done when you're getting screamed at I know!)
So set five or six simple rules - like, speak politely to everyone. During the day whenever you notice him keeping a rule give him some form of little reward, like a sticker on a chart or a marble in a jar, and when he builds some up give a bigger reward. Lots and lots of praise for doing the right things.
If he starts to break a rule, remind him of it. If he continues what you then need is a "sliding scale" of small deterrents, to be decided as best fits your child. For example, ten mins in your room, or no TV today, or whatever works best for you. If he continues, go up the scale. But think of them as consequences of his actions, rather than you punishing him - ie he is choosing to break the rule and therefore choosing that consequence.
I based this on a behaviour system used in my first school and have found it works wonders! The clear rules help you all know what's expected, and with rewards (and consequences) spelled out you always feel in control. Plus, the emphasis is on saying to the child, well you chose to break that rule, so you as the adult aren't the "bad guy" either.
Re the tantrums with any luck he won't get that far but if he does, there are several ways to deal with them. I think the key is what is the tantrum over? With my DD she actually weirdly kind of enjoyed them and also was using them to get my attention, even in a negative way! Once I finally worked that out, I discovered simply totally ignoring her was the answer - the screams upset me so I put my music on and read a book. First time she screamed for 20 mins, the second about three, then she never bothered again. (She was 6.5 too.) Also - does he scream in school? If not, why not? It struck me if she could behave in school there was no need to tantrum at home either.
Hope something in there is useful - do adapt for whatever best suits you though, and good luck! :-)