The last ability of Jace's Phantasm constantly monitors each opponent's graveyard to see if the bonus applies. If the stated condition becomes no longer true, the bonus immediately stops applying.

If Jace's Phantasm is dealt lethal damage at the same time as an opponent's creature, and that creature will become that opponent's tenth card in their graveyard, Jace's Phantasm will be destroyed before it gets +4/+4. This is because all creatures that have been dealt lethal damage are destroyed at the same time.

In a multiplayer game, a single opponent must have ten or more cards in their graveyard for the bonus to apply, although this opponent may change over the course of the game. You don't have to pick a single opponent; the ability will monitor each opponent's graveyard.