You should use the stackedplot with an output argument:
handle = stackedplot(rand(5));
Then you can use the handle to change the properties of your figure:
handle.AxesProperties(1).YLimits = [0 12000];
or in a for loop to change them all:
for i = 1:numel(handle.AxesProperties)
handle.AxesProperties(i).YLimits = [0 12000];
This does not quite control the ticks, instead it changes the limits of the axis, such as ylim([a b]) would do.
I do not think there is any property for stackedplot to do what you want, but this approach may suffice. Otherwise, I recommend you to use subplot and simply remove the xaxis of each subplot except for the last one.
for i = 1:5
h = subplot(5,1,i);
if i < 5, h.XTick = ;end
Then you can do what you want:
h.YTick = [0:4000:12000];
I think using subplot is a much better practice, because it gives you much more freedom.