Aside from the question of what the individual who travels to Eretz Yisrael when they have already started saying tein tal u'matar but we haven't should do in his tefilah, there is a question of what residents of an entire country that does not need rain should do when everyone else in the world has started saying tein tal u'matar. What do you do if you live in Australia, when the seasons are the reverse of ours?
The Rambam (Tefilah 2:17) paskens (based on Ta'anis 14) that if a particular place needs rain when other areas do not, the residents of that place should insert their request for rain in shome'a tefilah, where bakashos of individuals are inserted, but not in bareich aleinu. The takanah of saying tein tal u'matar in bareich aleinu is based on general seasonal patterns and is not adjusted based on particular need. Yet, the Rambam in Peirush HaMishnayos in Ta'anis acknowledges that in certain areas, asking for rain at the time of year in which tein tal u'matar is normally recited is nothing less than dangerous -- if our prayers were answered, it would result in a seasonal aberration. Apparently the Rambam does allow for adjusting when tein tal u'matar is recited based on the climate of the particular locale. The Kesef Mishna and Shu"T haRos"h both point out the apparent contradiction.
R' Shmuel Vosner (Sheivet haLevi I:21) writes that he thinks the Rambam makes perfect sense. The Rambam in Hil Tefilah is speaking about a location that by and large follows what we think of as the normal climate pattern. However, things can be a little off -- there might be a particularly dry year, a particularly wet year, and that place may need an extra bakasha to meet its needs. In that case, writes the Rambam, thebakasha belongs in shome'a tefilah. The Rambam in Peirush haMishnayos, however, is speaking about Australia -- a place where what we think of as the "normal" climate pattern is completely reversed. It doesn't make sense in that case to put the addition of tein tal u'matar in bareich aleinu at the same time as Northern hemisphere countries.
Many other gedolim discuss this issue and disagree (e.g. the Minchas Yitzchak), but R' Wosner is convinced his pshat in Rambam is correct, even though he hedges his bets a bit halacha l'ma'aseh in his teshuvos.