by shnar
You don't have to stop. You can move to an unexplored edge and move away to your hearts delight (assuming you have movement points).The rule for revealing tiles has nothing to do with movement. The rule is that in the Exploration Phase (a completely different phase), if your figure is on an unexplored edge, then place a tile. A lot of this was done in name of ease-of-play and balance. If you play that the monster comes out while you're still moving, that means you can attack it the same turn, before the monster attacks you, and then the game becomes incredibly easy.
If you wish to house-rule your game, by all means do so. There are a few similar such mods in the Variants forum (they tend to call them "initiative" systems). Take a look at them and tweak to how you'd prefer to play.
-shnar