I don't have time to look at the pattern right now, but these are my initial impressions:
Are you knitting the small version or the large version? It sounds like the "evenly" direction is referring to the 60 st cast-on (4 x 15 = 60). For the 70 st cast-on, I'd check the rest of the pattern and see if a 15-20-15-20 distribution would be OK.
I wouldn't recommend using the 4 needles unless the pattern was easy enough to convert. For example, half the stitches on one needle and a quarter of the stitches on the other 2 needles.