How does Movement work - is it a single Action (out of five)? Probably not, if adding two Movement Points is an Action. Does a player move all their units and uses up 5 Actions and then the game transfer to the other player?
The movement cost per hex is on the map page under the word Samurai, in the gray box. You can spend 1 action of the 5 to get 2 movement points. You can do this multiple times. Cross River -2 MP/Hex, Mountains -3 MP/Hex, Plains -1 MP/Hex.
You can spend Action points in any manner you wish from the 3 choices in the Actions section of the rules.
Actions (5 per turn per player)
Action Effect
Cost
1 Place 1 Chit of choice from your pool of chits.
1 +2 Movement Points
1 Initiate Combat Using 1 Chit.
Once all Action point are spent, then the next player takes their turn using the same method.
I hope this makes it more clear?