Knowing what the customer sees helps you answer "where is my gift?" in one reply. Here is the whole flow and what it leaves on the order.
What the customer sees
Once their order's subtotal reaches your minimum, a Free gift section appears in the Tacey block ("Make changes to your order") on the Thank you page and the Order status page, above any Recommended for you products.
Each gift is a card: the product photo, its name, its normal price crossed out and zero beside it in the currency the customer paid in, and a Claim now button (you can change those words under Gift button text in the tool's settings).
They tap Claim now (the button then reads Chosen), then Review the amount. The review step repeats the gift with its photo and zero price.
They tap Confirm and save. The gift is added to their order and the page says Added to your order and Nothing further is owed. There is no checkout and no payment step.
The text is shown in the customer's language.
What the order shows
The gift is a new line on the same order, quantity 1, with a 100% discount so its price is zero.
Because it is a real product line, Shopify handles its inventory, fulfilment and tax the same way it handles every other item. Your fulfilment app sees it like any other line.
Tacey does not send Shopify's "your order was updated" email, because the customer is already on the page.
The addition is written to your Ledger like every other change.
How many gifts a customer can claim
Gifts per order (1 by default) caps how many gifts one order can carry. Once an order has reached the cap, the offer is not shown again, even if the customer reloads the page. A customer who still has an old copy of the page open and taps Claim now again sees "We could not update this order" and nothing is added: Shopify refuses the same product twice, and Tacey refuses anything past the cap. If Tacey cannot confirm how many gifts an order already has, it refuses rather than risk giving a second one.
A customer can only claim a product you chose as a gift. Asking for any other product is refused, even if someone sends the request directly.
Stock and markets
Before adding a gift, Tacey checks it fresh with Shopify:
the product must be Active or Unlisted (never Draft or Archived),
the option must be available for sale,
the product must be sold in the customer's market, judged by the order's shipping country, or billing country if there is no shipping address,
one unit must be in stock, following your Shopify inventory settings.
Gifts that are not for sale, or not sold in the customer's market, are left out of the list. If a gift becomes unavailable between showing and adding, the customer sees "That gift is out of stock right now. Pick another one, or check back later." or "That gift is not available at the moment. Pick another one." There is no setting to give a gift you cannot ship.
What this does NOT do
It does not add a gift automatically. The customer taps Claim now on the gift they want and confirms.
It does not ask for payment or add shipping.
It is not offered on orders that carry import duties. Shopify can add a duty to the gift line of a cross-border order, so the gift is left out rather than leave the customer with a balance. A cross-border order that carries no duty yet can still gain one when the gift is added. By default the gift is offered anyway. Before they press Claim now, a customer on an order that ships to another country reads one sentence under the gift: Shopify may add an import duty when the gift is added, so the order may owe money (it is shown in their language, and never on an order that ships within one country or where Tacey cannot read both countries). If Shopify does add a charge, the customer is told the amount on the page and you are told in the edit feed and on the order's record. If you would rather never take that chance, choose Do not offer a gift on orders that ship to another country in the gift settings.
It does not hide a listed gift from your storefront. Set gift products to Unlisted in Shopify (Products, open the product, Status, Unlisted) so they stay out of your search, collections and recommendations.
Unlisted does not stop a purchase. Anyone with the product's direct link can still buy it at its normal price, because that is how Shopify built Unlisted (Shopify: Unlisted product status). A handle that is hard to guess makes the link harder to find.
A gift with no photo shows as text only. Add a photo to each gift product so the card looks right.
Free gift or Recommended for you?
They sit one under the other in the same block, each under its own heading, and they do different jobs. Free gift gives the customer a product you chose at no charge, once their order reaches your minimum; nothing is paid. Recommended for you suggests products the customer can add and pay for, optionally with a percentage off that you set. A customer can pick a gift and a recommended product in the same visit and confirm both together; only the recommended product can leave an amount to pay.
Frequently asked
Can the customer choose a size or colour of the gift?
Only the options you picked. Each option you add under Gift products shows as its own choice.
Is the gift taxed?
Tax is worked out by Shopify, as for any line on the order. The gift line's price is discounted to zero.
To set the tool up, read how to offer a free gift after checkout. If the gift is not appearing for a customer, use the checklist in why the free gift is not showing.