Nero was described by Suetonius as not only using poison, but provided the woman, Lucusta, from whom he'd acquired poison with which he killed Brittanicus with a full pardon, large estates, and sent her students (Life of Nero 33.3). Lucusta was being paid to teach toxicology to students; a job we see in various universities today, though it usually seeks a different outcome.
I chose Nero because everyone knows him. One of the police officers who was helping the march along asked me "who's Nero?" I prepared to go completely crazy when he said "just kidding!" There are better examples of toxicological research. Most famously, Mithridates of Pontus was best known for his toxicological research, trying to find ways to both protect himself from poisons or poison himself (I've written about this elsewhere). Cleopatra was also well known for her toxicological research. Although it is a later source, Plutarch (Life of Antony, 71) even provides descriptions of her use of prisoners sentenced to death to conduct human experiments to determine which poisons worked best.
I went to a lecture a couple of years back in which a Medievalist stated that science experimentations did not occur until the 11th century, yet this does not reflect the language of ancient medical texts. Medical writers would describe treatments as "those which I have tried by experimentation."* Phrases occasionally used include "Some say to do [this], but I have never tried it myself."* Looking at Galen's lists of compound drugs, he often states whose recipe it is, thus providing us with ancient examples of citations in relation to medical research.*
Yes, science experiments were conducted in antiquity. Yes, people were paid to teach a variety of sciences in antiquity. Yes, scholars provided citations to other scientists in antiquity. Even ancient scientific writings formed the basis of many modern sciences. Ancient history has a roll in modern science, and this ancient historian attended yesterday. I certainly hope there were more.
*Yes, I should provide proper citations for these, but to quote a sign photographed and posted on Twitter yesterday: "I should be writing" something other than this blog.