If data was split before scaling then...
Normalized: the min and max (eg 0 and 1, or -1 and +1) should be present in the training data. (Not so for test or application data.)
Standardized: the training data should be standard normal, ie pass is_standard_normal() (in particular, should have mean close to 0 and stdev of 1).
See also #6
OTOH, if scale then split...
Normalized: probably can't tell unless min or max happens to be in test split.
Standardized: For the mean, I think can check if that gets closer to 0, as long as we know how many training samples there were. For stdev, then possible to tell only by putting all the data together? Seems expensive.