As per my understanding, you want to create a rectangular pulse with x=0 at t=0. The reason behind why you are not getting x=0 at t=0 is that you have mentioned pulseperiods = [0 0.12 0.24 0.36 0.48], which means the first pulse will be at x=0 with x=pulsewidth/2 at t=0.
One possible workaround would be to start the pulse from x=0 by offsetting the pulse period with (pulsewidth/1.999). Note that if you would shift by exactly (pulsewidth/2) then you would get x=1 at t=0. To avoid the same, it would be preferrable to offset by a number slightly greater than half of the pulsewidth.
The implementation would look something like this: -
Fs = 1e9;
t = 0:1/Fs:(4*1200e-9);
pulsewidth = 200e-9;
pulseperiods = [0:4]*1200e-9 + pulsewidth/1.999;
x = pulstran(t,pulseperiods,@rectpuls,pulsewidth);