Sounds about right. Looking at other vendors, they have 50cm strips of 36 LED, each LED quoted at 0.3W, so 72led/m x 0.3W/led = 21.6W/m
350W is ok, but at 12V, that's 30 amps, which is quite a bit. You will likely have to use multiple 12V outputs of your PSU (check the ratings) and carefully pick your wire gauge to reduce IR drop (and also keep wire temp low).