[xyz]tick controls the number of major tick intervals to draw for the axis. If you want to display 4 major ticks (so 3 intervals) you need to set this value to 3 (not 4).
I made a test on IDL 8.2.3 and the commands below give the same result in terms of number of tick marks.
plot,findgen(10)
axis, 1, yaxis=0, /save, yrange=[0, 10], ystyle=1, yticks=3, $
yminor=5, color=140,ytickformat='(I)'
plot,findgen(10)
axis, 1, yaxis=0, /save, yrange=[0, 10], ystyle=1, yticks=3, $
yminor=5, color=140
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