If I give an action token to an opposing character that has no tokens using this power, and that character takes an action later from either incapacitate or taking an action on it's own, does that cause pushing damage?

Yes, since those later tokens that cause the pushing damage would not come from this power.

VP is correct. The key phrase in the power is "THESE tokens"; in other words, if these tokens would cause a click of push damage, ignore it. If tokens from a later source caused a push, well, we are back to our regular broadcast... HEADS UP!

But wouldn't the next tokens cause pushing damage because of the tokens from this SP? And therefore, indirectly, pushing damage was caused by those tokens, and should be ignored?

Yes they are involved with the pushing damage. however, they do not cause the pushing damage therefore is not ignored.

Though you have to remember that the previews are not the finished product, they could easily change the wording on the power before it is released

The second tokens cause pushing damage because the character had tokens on them already.
Are you also arguing that the characters assigned these tokens should be able to push on their turn and not take pushing damage?

If it was intended that a character not be allowed to take pushing damage because of these tokens in any way then they could have said "any characters assigned one of these tokens are immune to push damage until the beginning of your next turn" or something.

It's the same argument as a mystic taking pushing damage from an incapacitate attack.
The incapacitating character doesn't take mystics damage because the attack didn't cause damage. The argument that the attack did cause damage because it forced the mystic to push doesn't stand up.

No. Pushing damage is only ever checked when the tokens are actually placed; you can't retroactively apply pushing damage. Otherwise, when you damage a Willpower character with two tokens, knocking it off Willpower, it would suddenly take a click of damage for pushing at some point in the past.

In this case, when you apply the tokens from this SP, you check to see if pushing would occur. If "yes", then you don't (per the wording of the SP). If "no", then there is no need to worry in the first place. And once those tokens are placed, they are action tokens like any other on the map.