You're more generous with screen time than Michelle Obama- she's harsh.
Most experts would suggest an hour a day of combined TV, gaming and/or recreational computer. They also suggest it happen well before bed as the blue light emitted by these devises can interfere with sleep.
On your son's reaction, maybe he was set on doing something and your "no" came unexpectedly. Perhaps it was exacerbated by being tired or other disappointments during the day that left him feeling a little out of control. That he got it back together is terrific.
The best approach is to be transparent in your expectations. Perhaps post or discuss a family rule about the use of electronics so everyone is on the same page. When DS was that age, we had time for about an hour or so on school days; like your kids he was able to entertain himself with reading, his model trains and building projects.
LOL, when Sandy came through, we lost our electronics for about 3 days and let me tell you, I was just as cranky as DS was. DS and I are computer addicts- I have forums and news, DS is all about facebook, forums and youtube sites. DH, who is really into TV, was teasing us both. Joke was on him though, the power surges blew out his cable box and he was "out" another 2 days after we got our connections back.