Really: It is correct that every Astrolabium dial is calibrated to a specific latitudinal position on the globe. The reason for this lies in the different durations of dusk and dawn (the nearer to the equator you are located, the shorter these phases are, so the appropriate zones on the dial are thinner), but also in the different projection of the equator (the curve is steeper the more to the South you are located).
As a result, you need a different dial whenever you change your latitudinal position, move to the North or the South. Ulysse Nardin can print a new dial for every latitude. BUT: If you calculate the scale of the dial, compared with the size of the world's hemisphere, you will realize that you have to change your latitudinal position very considerably, before you can make out the difference between the two correct dial variants with the naked eye. When moving from New York to Paris, I can assure you, would introduce a very neglible difference, so I see no reason to have the dial changed.
The longitudinal factor is different, but the necessary changes to the Astrolabium's mechanism can be easily executed by yourself.
For the projection of the stars, the longitudinal position on the Earth is irrelevant. But it is important for the calculation of the times of the stars rising over the horizon, and the times of sunrise and sunset. For reading that serves the sun hand, which turns once in 24 hours. This sun hand shows the true solar time in your location, that is the time when 12 o'clock noon is when the sun is in the zenith. When you travel east- or westward, this time of course changes, so you have to adapt the sun hand display. You can calculate this solar time in your planned destination yourself: Imagine that the GMT or Greenwich time is the time when at exactly 12 o'clock noon, the sun is in the zenith over the 0 meridian in Greenwich. For every degree difference in the position from the 0 meridian to the East or the West, you have to add or to withdraw 4 minutes. Now find out the longitudinal position of your future location, there are many ways to do it, with Google Eaqrth, for example. Then calculate the true solar time there, by deducting or adding the minutes, starting with the zero meridian as reference.
Without having to do your own calculations, you can use websites that help you, like this one: