I believe this refers to gaining movement points during another figure's activation. In this case, you spend any actions gained immediately so the active player can continue his play.
Correct. If any figure gains movement points outside of it's normal activation for any reason, it must immediately spend them and any unspent points are then lost.
During your activation, any movement points granted by action cards can be spent at any time during your activation (except during an attack) but any special text or attacks granted by a card must be resolved before you play another card.
For example: Let's say you have 2 copies of "Up Close & Personal (Super Shotgun)" in your hand. Playing your first copy grants you 4 movement points. You may spend them now or save them for later, or both. Then you must perform the attack listed on the card or lose it. You cannot "save the attack for later", play your second copy and then get 8 movement points before making 2 shotgun attacks.
So, again, movement points can be spent at any time during your activation. Special text and attacks on action cards must be used when the card is played.