No. As of February 2020, for both the Pay as you go plan AND the Unlimited plan only the Source store is charged for copies.
What if I have multiple stores I'm copying to?
While the price DOES increase for each additional store you are copying to - we still only charge the original, source account for all of your copies.
"How do I know which plan to subscribe to?"
Deciding which paid plan you should subscribe your stores to is dependent upon your use-case and intentions with Replay:
If you only intend to make a one-time copy or intermittent copies, you should subscribe any and all stores being copied to/from to our Pay As You Go Plan.
If you intend to make many copies, wish to setup a continuous, ongoing copy, and/or wish to copy Product Metadata, you'll need to subscribe any and all stores being copied to/from to our Unlimited plan.