Trek has never showed lightspeed (that is, instantaneous) beams: the ones from TOS generally traveled slowly enough for the eye to see, which is very
slowly, even when dialogue suggested they were hitting targets that were moving at FTL speeds themselves (say, "Ultimate Computer").
What is unusual about the beams from the 2258 era of the eleventh movie is that they are fairly short, "Defiant
length" pulses, whereas the pulses in ST2:TWoK were rather longer and the beams in TOS and TNG tended to dwell for several seconds and never flaunt their rear ends to the camera much. The pulses from the 2233 era of the movie were quite a bit longer, closer to what we saw in TOS or ST2.
Didn't the Kelvin fire beams at the Narada?
Well, good question. We don't know where Robau or Kirk aimed their red beams, but dialogue indicated that they (like the white bolts) were being used purely defensively, to parry Nero's projectiles. We never saw a beam hit the enemy ship proper, and the first damage experienced by the Narada
in terms of dialogue or visuals or storyline was when Kirk rammed the Starfleet ship into her.