As has been said, the Bronze tip started it. A Canadian bullet was the first with a poly/resin/plastic/whatever tip but I don't have a reference book within 1800 miles to tell you its name. The old time reason was to protect bullet tips from deformation during recoil. When high BC bullets suddenly became ultra important the focus changed to being slippery in air. Mechanically, the plastic tip drives back into the core of the bullet initiating expansion. Tipped bullets begin to expand more quickly than soft points, requiring an adjustment to the jacket design. The reason there is a Sirocco II these days is a further re-design of the jacket shape to control expansion and increase penetration.
I firmly believe that the reason tipped bullets sell so well is not how they perform inside animals but how they perform in the heads of shooters. A bright red tip on a SST is sexy as all heck! They look accurate. They look fast. They look deadly.
Usually when you meet a guy who refuses to shoot plastic tipped bullets he has heard (less often experienced) that plastic tipped bullets blow up on game. Early tipped bullets did have that problem on occasion. Fact of the matter is, no matter what is leading the charge, it is the jacket that is the most important part. Starting expansion is easy, controlling it is the tough part.
If you're interested in bullet design and terminal performance, I would encourage you to look for "Rifle Bullets For The Hunter - A Definitive Study", compiled by Richard Mann and including many knowledgeable gun writers. Also, call and ask some questions of bullet manufacturers. Sierra has been very informative and patient with my questions in the past.