Lower Ascent.

What determines if you end up in the Valley of Heroes I or Lower Ascent after falling off the map?

If you're refering to a fall from the Lower Ascent map itself, it's the fact that some other command overrode the -sends you to Valley of Hero 1- command, which can be:

• A pot usage: pet food, HP/MP pot, whatever pot..
  
• A skill usage: Booster, HB, MG, whatever skill...
  
• Some other factor but I forgot for now.

The above listed commands need to be inputted at the correct moment, being exactly a few short moments before you pass the "out of bound" line, and last throughout the duration you pass that line. Practice makes perfect.

To better explain that, there's a 'instant transport' sort of thing at a certain point, as well as a sort of fail-safe a bit further below that, at the very bottom of the map. If you hit the fail-safe point, you get transported back to the map you're on, and the 'instant transport' takes you to where the game wants you to go.

You can prevent yourself from entering any portal by taking certain actions. The easiest way is to hotkey pet food and rapidly tap the button without having a pet out. You can also use this to, say, climb up to the top of the platform in Henesys Hunting Ground, or to end up below the main platform of the Orbis ship/climb back up from there without leaving.

Using pot to override commands have various use, one of the most interesting things to me is jumping as a dragon.

The other factors I mentioned include cc-ing, btw.

CCing saves you from auto-portals? Now that's something I didn't know.