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.
As per natal chart, you can always use heliocentric system, where Sun is in middle of the chart (so you don't see it as a glyph) and Earth and Moon are together. Though, I haven't seen many astrologers using this system ...