March gives LaCl3 and CeBr3 as additives which direct the reduction by NaBH4 or LiAlH4 to the C=O.
Other possible reagents: AlH3, Et3SiH, NaBH3(OAc), LiB(Bu)H3, DIBALH.
I guess that when you write 'conjugate reduction', you actually mean 'double' reduction, because it seems that you end with both the C=C and the C=O bonds reduced.
If that's the case, in principle you don't know which is reduced first (although one path is more likely to be correct). So in theory if you quench a sample of your reaction mixture you can have variable amounts of: C=CH-C=O, CH-CH2-C=O, C=CH-CH-OH and CH-CH2-CH-OH.
If you monitor these species, you may understand something more about the kinetics and then vary your reaction conditions accordingly.
If you only look at the result after 12 or 24 h, i.e. a single point, it's harder to optimise the method.
Btw, why doesn't she want you to use LiAlH4, if I may ask?