The logic of the likert scales itens codification that you used is correct. All itens should be the same "direction", because the process of analysis is "mathematic". If you used the negative itens with it original codes, the correlations will be also negatives or They showed with incoerences in the factorial loads.
A reference is: Hair, J., Black, W.C., Babin, B.J., & Anderson, R.E. (2010). Multivariate Data Analysis (7th Edition). Pearson .
Just adding to Dirceu's points, reverse coding your items is not a choice, rather it's a requirement to have standardized scores. Even reference is not required in this case, but you are always welcome to do so.