If defensive lineman jumps into neutral zone then offensive player moves directly after, is the penalty always on offense?

Where is the offensive player that moves in relation to the defensive player in the neutral zone? That is the question...

If he is immediately "threatened" by the defensive player in the neutral zone, then it is offsides on the defense. If the offensive player that moves is not threatened then it is false start on the offense.

So say the defensive tackle jumps into the neutral zone and the offensive guard immediately in front of him moves in reaction, it is offsides, defense. If the defensive tackle jumps into the neutral zone and the WR moves then it is false start on offense, same thing for the guard on the other side of the center if he were to move.

The defensive player has the opportunity to get back on their side of the neutral zone before the ball is snapped with no penalty, as long as they don't make contact with any offensive player.

Fencewire is correct. The term threatened is used in the rule book. By rule, a maximum of 3 players can be threatened depending on where the defensive player is lined up. If he is lined up in a gap, then only the player to his right and left of the gap could be threatened. If he is lined up directly in front of a player, then the player he is lined up in front of, as well as the player to the right and left could be threatened. If very important to also realize that sometimes the defense will jump, but not enter the neutral zone, causing an offensive player to react. This would not be offside, but instead it is false start. Entering the neutral zone is the key.