Triannon technology was vastly inferior to that of the 22nd century Starfleet; it took one of their ships a year to travel 6.3 light years. They did not have transporters, nor did they have any experience with them.
The Triannons had a strong religious faith; they believed that the Delphic Expanse spheres were created by gods they called the Makers. They believed the Expanse was the "Chosen Realm" of the Makers, who were supposedly using the spatial anomalies ("the Makers' Breath") to reshape space to create a paradise in anticipation of their eventual return. They claimed there were thousands of spheres, though more scientific Xindi analyses showed that there were 78.
The Triannons venerated the spheres through prayers and meditation, often taking pilgrimages months long to see them. However, traveling through a sphere's cloaking barrier, landing on it, or going inside it were all terrible acts of desecration punishable by death. They stated upon boarding Enterprise NX-01 that among their many beliefs included an aversion to invasive medical care; they did not allow detailed bioscans, but this might have been a ploy to avoid detection of the organic explosives embedded within their bodies.
In the mid-21st century, a religious war broke out on Triannon between the major factions of their religion. One faction (an influential member of which was Pri'Nam D'Jamat) believed the Chosen Realm was created in nine days; this faction is indicated by red tattoos on the right side of the face. The other faction believes the creation took ten days; they bear black markings on the left of the face.
The group of Triannons serving on D'Jamat's ship was unaware of this, however, as they had been on a pilgrimage to the 12th sphere. In November of that year, they hijacked Enterprise using powerful organic explosives laced within their bodies. D'Jamat planned to use the powerful starship to end the war once and for all, but following a brief battle with the "heretics" the Enterprise crew successfully took the ship back and returned D'Jamat to his homeworld, showing him what had happened to it. (ENT: "Chosen Realm")