Can I get both rewards from an Invasion?
Solution 1:
No, on each mission you will have to choose a faction to support.
Changing the faction you have supported will subtract from your progress on the original faction until you are back to 0 before adding to the other faction.
So if you complete the mission 5 times for one faction and then 1 time for the other faction, you will be at 4 missions completed for the faction you first did missions for.
And since the reward is not paid out before the node is resolved (100% to one faction), you will not be able to get rewards from both sides even if you play 5 missions for one side and then 10 missions for the other side (I have tried it).
For the event they had where your total missions for a faction counted towards getting special rewards like weapons they said that you would have to have an uneven number of wins, doing 50 for each side would not get you on a winning side even though you then had complete 100 missions.