Nope, dtilt doesn't put them in jab position. Tripping them won't put them in jab position either, if you were thinking of Diddy. What happens when they trip is that any interaction with them counts as if they were standing, except their options have been reduced to those of a character that didn't tech and faceplanted.
Jab position, as far as I know, is when the opponent falls flat on his ace, and has the options to roll away, stand on spot, or get up with an attack. A trip has this limit, but they're not laying down on the floor, so once you hit them, they stand up.
Dair is the easiest way to force your opponent into jab position AND fall right next to them in a small fraction of a second, enough to start your first jab, commencing said jab-lock... Which, in turn, leads to an easier-than-normal kill, and if you fail the jab, since it's a fast animation, your opponent won't have time to punish you after rolling away, which also means it's safe.