From what was said by someone who played a demo:
2 general rules: You alternate with your oponent when possible, inside a tick or when going from one tick to the other. You play your figs when you are the only one who has figs left on a given tick.
When the game begins, each player trows a dice, and someone (probably the highest) starts. Then you alternate players. (For the first tick, everone acts since everyone probably starts at tick 1). (Example: B wins the roll, so it goes like this B, A, B, A.)
In future ticks, you continue to alternate. For example, everyone (most likely) only moved on tick 1, so they are all now on tick 2. If player A played last on tick 1, player B will start tick 2. (In the above example, tick 2 will also go like this B, A, B, A)
If a player has no one on a given tick, the other player plays whatever he has on that tick. (On tick 3, one of A2 acted for 3 ticks, that brought him on tick 5, A1only moved and is now on tick 3; B1 and B2 both acted for 2 ticks, so they are both on tick 4. At tick 3, A1 acts even if player A is the one who played last on tick 2. Say he asts for 4 ticks, and is now on tick 7.)
If one player has more than one fig left after the alternating pattern is trough, the other player plays all he as left. (Example: On tick 4, B has both figs, and A has none. So B starts and then play his second fig. Say both only move, so they are now both on tick 5 with A2. Then since B finished tick 4, A will start tick 5 with A2. Then B will play both his figs.)
I think I covered all possibilities. Again, this is from another post I read here, by someone who played the demo.
EDIT: Another comment: So you don't have to remmeber which fig acted first or last, only which player played last.