From the FAQ:
If a creature with reach, such as an assassin vine, grapples you, it then pulls you into its space. Does this move happen all at once or is there a limit to how far you are pulled in a round?
When an attacker grapples, the attacker must move into the defender’s space, not the other way around. If you can reach a foe and you establish a hold, you move into the foe’s space as part of the grapple attack; this movement is free and doesn’t count against your movement for the turn (see Starting a Grapple in Chapter 8 of the Player’s Handbook).
A monster with the Improved Grab special attack, such as an assassin vine, pulls the foe into its own space rather than moving into the foe’s space (see the Improved Grab entry in the
Monster Manual glossary). This is also part of the attack and does not count as part of the attacker’s or defender’s movement.
(Emphasis Added)