Warp drives in Star Trek are a fictional version of the real-world physics concept of the Alcubierre drive. From the Wikipedia article:
...Alcubierre proposed a way of changing the geometry of space by creating a wave which would cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand. The ship would then ride this wave inside a region of flat space known as a warp bubble, and would not move within this bubble, but instead be carried along as the region itself moves as a consequence of the actions of the drive.
The energy costs of such a drive are difficult if not impossible to achieve, and even if those were overcome, implementing an Alcubierre drive might result in a very different setup than what one sees in Star Trek. However, both this article and the Memory Alpha articles on warp drive do not address whether or not a starship traveling at Warp Drive would intersect matter in normal space, such as an atmosphere. Given the sprawling nature of Star Trek canon, if such an explanation exists, it's possible that there's another one that contradicts it!
However, there is one clue that may help us here: Starships in the Star Trek universe are all equipped with a navigational deflector:
The navigational deflector... is used to deflect space debris, asteroids, microscopic particles and other objects that might collide with the ship. At warp speed the deflector is virtually indispensable for most starships as even the most minute particle can cause serious damage to a ship when it is traveling at superluminal velocities.
A starship is riding inside a warp bubble, which is possibly outside of normal space (although I can't confirm or deny this). Either way, it's fairly clear that they can see and interact with the universe outside of their warp bubble.
Since a deflector dish is a fairly prominent part of a starship, one can make the reasoned assumption that these dishes and their subsystems would have to be fairly powerful to reach across vast distances as well as quick, to react to pieces of matter approaching the ship at warp speeds. (On the other hand, smaller warp-capable ships, such as shuttlecraft, often have no visible navigational deflector, so perhaps these systems get exponentially larger as ship size increases.)
Going back to your original question about the Enterprise coming out of warp in Titan's atmosphere, it's safe to say that the ship's navigational deflector took care of pushing the atmosphere out of the ship's way. However, these systems are designed to handle space dust and small asteroids while traveling in (mostly) empty space, so a planetary atmosphere would probably put a big strain on the system, and might even be dangerous to the ship.
In conclusion, I'd guess that a starship could enter or exit warp in an atmosphere, but would probably prefer to not put such a large strain on it's navigational deflector except in emergency situations.