Maybe there's a clean way to approach paradox issues (e.g. the universe course corrects), maybe it can be completely side-stepped, or maybe it can be swept under the rug.
Honestly, if technology is the reason for time travel, and if all information about NLT is available throughout the whole span of time that it exists, then it could very easily be something built into the technology that makes it possible in the first place. The tracker one wears would have a kind of paradox-avoidance feature that keeps one from going to a place/time they've already been, or from encountering any situation that would otherwise divide by zero.
"So, Bob, I was going to attend your son's first birthday party, but my paradox-avoidance ring went off. Apparently, your son had a dog that dug up a sapling. If I go to your son's party, you don't end up buying that exact dog for him, that sapling would end up growing into a tree that falls on my grandmother's house, somehow preventing my birth. Sorry about that, bud."
Perhaps it could work quietly in the background. The act of avoidance could be felt like an inconvenient detour. "Damn red light."