First, some disambiguation.
Exotic matter was the term used in Morris and Thorne's 1988 paper on wormholes to describe mass/energy with a negative stress-energy tensor. Later refinements codified this as mass/energy that violates the Averaged Null-Energy Condition (ANEC), which is described in detail on page 6 of reference .
Exotic matter can also refer to such strange states of matter as charmonium, pentaquarks, magmatter, Q-balls, and their ilk.
With respect to wormholes, exotic matter means mass/energy that violates ANEC. The term "negative stress-energy tensor fields" is more technically accurate and precise, and less likely to be confused with the other forms of exotic matter. It also seems to be a term only a physicist would use. ;-)