My understanding, formed after much guesswork, is that "hand colored" meant different things to different publishers at different times.
1) That "hand colored" meant that a water-color-type 'wash' was applied, one card at a time, by a hand-held brush. These might best be detected by noting that any one color shifts in different directions in different parts of the card, eg, on the left side of the image it is applied a little high, while on the right side of the image it is applied a little too far to the right.
This sort of hand-tinting was especially common after WW1, when there were legions of one-armed men available for menial employment.
2) The same, but with the assistance of a mask (or template or stencil). In this case, in the event of misregistration, a single color would be shifted in the same direction in every part of the image.
It would not do to underestimate the ability of a one-armed man to set a mask, paint, remove the mask, etc.https://en.wikipedia.org/wiki/Paul_Wittgenstein
... Paul Wittgenstein (November 5, 1887 – March 3, 1961) was an Austrian-American concert pianist notable for commissioning new piano concerti for the left hand alone, following the amputation of his right arm during the First World War. He devised novel techniques, including pedal and hand-movement combinations, that allowed him to play chords previously regarded as impossible for a five-fingered pianist.
3) But the same term ('hand colored') might also be applied to colors that were applied mechanically (eg by a separate pass thru a press) because the plates were, after all, drawn by hand.
In Europe, in the decades after WW1, there was a handful of publishers of very high resolution black'n'white photographic postcards mass-produced on a rotary press. Some of these cards were tinted (a/k/a colorized), and I've seen both a) cards that were clearly tinted one-by-one, literally by a hand-held brush, and b) cards that were clearly tinted with a mask or a mechanical process.
While I will ass-u-me that collectors who really care have a consistent nomenclature to distinguish all of these different processes from one another, I am also really, really sure that the publishers pretty much used whatever term appealed to them and that, some times, it can be really, really hard to tell one process from another.
Remember that the publishers might have seen a commercial advantage in allowing customers to think that they were employing an army of wounded veterans long after they'd sent them all packing.
In this particular card, I notice that the dome of the building is tinted green - and that the shore/beach line is consistently tinted green - and would, therefor, rule-out free-hand tinting.
Q/ But how would you tell the difference between tint applied with a brush-and-mask versus tint applied by a plate-in-a-press?
I've thrown this question at postcard dealers at shows, and they all agree ... to shrug.