Yes, they should be vice-versa.
If a textbook is using an upper-case/lower-case system (as many do), UC Roman Numerals mean Major (and Augmented with +) and LC Roman Numerals mean minor (and diminished with o).
In the key of C,
i is C minor
I is C Major
iv is f minor
IV is F major
etc.
Now, if you're calling I IV and V the "primary triads", the the remaining triads might be called "secondary" - I usually hear "primary", but no mention is made that the others are necessarily "secondary" - but there are people always trying to compare them to the colors of the rainbow and this and that and the other.
I IV and V = Primary
ii iii vi and viio are secondary.
IN A MAJOR KEY, ii, iii and vi are ALWAYs minor, and viio is ALWAYS diminished.
I IV and V are ALWAYS Major.
The only exception is when you use mode mixture.
In minor keys,
i iv and V are Primary (note, V not v).
iio III VI, VII and viio are secondary.
As you can see III and VI are ALWAYS Major.
VII may be Major (VII), built on the subtonic, or diminished (viio) built on the leading tone.
iio is ALWAYS diminished.
i and iv are ALWAYS minor, and V is ALWAYS Major.
Again, mode mixture comes into play. Additionally, minor includes some other chords that are basically mode mixture, but so common in minor as to be considered part of the system - iv may be IV, and V may be v.
HTH
Steve