Principal components can be performed on (a) covariances or (b) correlations.  A PCA is performed on (a) covariances in order to take advantage of a larger importance to be given to variables with more variance.  Off hand, I don't think I have ever seen that option used in the social sciences. 
If you perform the PCA on (b) correlations, you get the same resultsfor factors as if you had used covariances on the standard-normal  transformed version of the data.  There is a minor advantage of having on hand those transformed data -- In my experience, I needed those transformed data in order to score up the theoretical factors using the factor-scoring coefficients. 
You don't ordinarily perform PCA on a longitudinal collection of data. Using the PCA from the "base" period is something that is sometimes done -- In that instance, you *would* standardize all the data for all periods by using the mean and SD for the baseline period, when you get around to scoring factors on all data.  "DO REPEAT" is useful for that. (Or -- Is there a way to get FACTOR to score up data that are to be omitted from the analysis? - I never knew one.)
If there is some other question arising around longitudinal and standardized data, you have to be more specific.