The birth-chart (aka radix-chart) of that person remains the same. A 90 year old still wears the particular "cosmic fingerprint" acquired at birth.

For predictions, astrologers use the horoscope of any particular time in the future called transit-charts, superimpose it onto a radix-chart and study the aspects these two charts form. I don't see a reason why the same principle shouldn't be applied to a date 100 years before a person was actually born. It would still be a prediction would it not, for these 100 years would still lie ahead of the time traveller? The transiting points would certainly form different aspects of his/her radix-chart. It would be interesting to see how an individual would experience this, for it would shatter the natural cycles he/she was living before.

But what about space travel? A human who is born, let's say, on Mars? There would be no Mars in that horoscope, but an earth. What would that mean for that human? Not to mention a birth taking place outside our solar system. Geo- and heliocentric astrology would definitely be rendered unusable.

Last, but not least, seen from our geocentric perspective, every planet has its retrograde phases.