Chasing after the power says...

R destory this foundation: After you make a control check, that control check gets +2. Only playable while commited.

Now let's say I play a 6 diff attack and check a 3. Could I commit Chasing after the power, and then respond with it's R? Or has the "After you make a control check" phase passed?

The trigger has passed, once you start committing foundations, in your example.

Okay. Thanks for that.

That's not actualy exactly correct (I think).

You could commit three foundations to make the control check successful, and then still respond w/ CATP to give your control check +3. Note that this would still only make the control check a 6, and you wouldn't be able to take back the committals. but it might be useful theoretically.

Wrong, you're beyond the point of modifying the check once you get to the point of committing foundations to pass it.

8.1.3.3 If the player’s check was less than the required difficulty, then they must either
commit enough foundations to make the check successful or fail the
control check and thus their attempt to play the card. (See 8.1.3.5)

Committing foundations only happens if the check, including modifications, is less than the needed value. Not at the same time as the modifications.

-Mr. Tinman