The only explanation I know for the Asian and Philippine practice is that around 1970, the Vatican gave permission for the use of the "chasu-alb", a weird-looking garment that is shaped like a thin white chasuble, but with the sides sewn up rather than open. This vestment was allowed for use by concelebrants in Masses celebrated inside churches, and by the main celebrant and concelebrants in Masses outside of churches. Naturally, when the chasu-alb is used the stole is put on top of it. Eventually, as liturgical training became more and more sloppy and as priests and bishops forgot a lot of fine distinctions, the practice was transferred even to those cases where the priest / bishop wears a proper chasuble.
Is it like that
http://www.aracaeli.com.br/fotosprodutos/tunica%20branca.jpg ?
Here in Brazil it's called "túnica". There is a permission to the clerics to use it. Some of them use the "túnica" with the stole during the week, and on Sunday they vest normally, with the chasuble.
In the Philippines that would be an alb. Chasuble alb is like this:
http://www.rcam.org/photogallery/holy_week_2009/chrism_mass/pages/pic25_JPG.htmThis picture is from the Chrism Mass of 2009 in Manila Cathedral. If you will look carefully, the "chasubles" (chasu-albs, really) are closed at the sides. Strangely, some priests are still wearing albs under the chasu-alb, while the others are not. Manila Cathedral is heavily airconditioned so the weather isn't a factor.
This is from the Liturgy Congress of 2009. Same things:
http://www.rcam.org/photogallery/2009_liturgy_congress/pages/pic39_JPG.htmIncidentally, this Congress "decreed" the abolition of the use of the alb or cassock with surplice for altar servers in Manila. Henceforth, altar servers are to vest in "barong" (either long-sleeved or short-sleeved), a white polo shirt made of native fibers:
http://www.mybarong.com/mens-barong...amp;sleeve=short&in_stock=1&ln=7Really, in many places in Brazil, the chasuble is worn only on Sundays? We don't have that, but Filipino clergy have a dispensation from Rome to no longer wear the amice and cincture, and to replace the alb with a white cassock or habit. In practice even the alb/cassock is frequently dispensed with.