The issue of payment is clearer in 53:3
For nothing you were sold,
without money you shall be redeemed.
My reading is that--as shown in v. 3--it is a future event, even though described in the past tense in v. 9. The prophet (whether one thinks of the historical Isaiah writing more than a century previously or Second Isaiah writing as the Exile was ending), calls Israel to rejoice because of her coming liberation from captivity. His use of the past tense emphasizes the certainty of the event from God's perspective, which is beyond time.
How was the redemption achieved: here the prophet portrays it as God's free gift. Elsewhere, he describes it in terms of Israel enduring punishment for sin, which has provoked God to wrath. After a certain period of Israel's penance, God is moved to forgive. This is expressed poignantly in Is. 54:
6 The Lord calls you back,
like a wife forsaken and grieved in spirit,
A wife married in youth and then cast off,
says your God.
7 For a brief moment I abandoned you,
but with great tenderness I will take you back.
8 In an outburst of wrath, for a moment
I hid my face from you;
But with enduring love I take pity on you,
says the Lord, your redeemer.
Conclusion: What has been redeemed? Israel, especially Jerusalem, from Babylonian captivity. How was this redemption achieved? By God's grace, after a period of suffering and repentance. Although the prophet describes this in the past tense, he is referring to a occurrence in the future, when the Jews returned to Jerusalem.