Using Event Cards to Move off Vine Walls
No, you do not have to roll for units that are removed from a Vine Wall if they do not move. The word move is a keyword in Summoner Wars, and unless the ability or event specifically uses it, the movement would not be considered a move. Note that during the movement phase, units move. 

This thread over on the Plaid Hat Games forums reiterates this: "Note that this only applies to 'moving'. Abilities that place a [card] somewhere are not affected by Vine Walls."