Yes, it does mean poisonous. But only the latex found in the tree and unripe fruit. Even so much that it is used to make arrow poison and as an insecticide.
For what it's worth, the scientific name of the common garden tomato means "Nightshade Wolf-Peach"
There's often a story buried in the scientific names. In the case of tomatoes, lots of Europeans were scared to consume them after they were introduced because of the clear resemblance to the poisonous black nightshade. In Germany and some other areas in Europe, there were also folk stories that connected the consumption of nightshades (and as a consequence, tomatoes) to lycanthropy. This slowed its acceptance in European cuisine. While introduced to Europe by the Spanish, it was the Italians that led to increasing acceptance of it as a food staple; in Italy there had been a long tradition of consuming
Atropa belladonna as an "oral cosmetic" (to make the skin pale, pupils dilate, and reduce the appetite), so this probably increased the ease of accepting tomatoes into the diet.
A bit off topic, but while we're on the topic of "scientific names of edible species that cast aspersions on their edibility..."