The system was called UzKart (do not confuse with UzCard, which is modern online successor of that system). On the day when salary was paid, you had to find an online ATM or internet-connected terminal in the shop, and "load" money to the card. Then, you could use the money on the card to pay in offline terminals. Balance could be checked directly in offline terminals, you had to ask the seller to print it.
Sellers had a special offline card, called "merchant's card". In the end of the day they loaded all the transactions from an offline terminal to a merchant's card, and then brought the card to an ATM or a connected terminal, to synchronize payments with the bank account.
If, for some reason, at the time of synchronization some payments failed to clear, payer's card was banned and they had an angry call from the bank.
When the system was introduced, internet connection was expensive and unreliable. It co-existed with online cards, but merchants strongly preferred to deal with offline cards. As soon as mobile internet become cheaper and more widespread, offline cards died because of the hassle with "loading" and "unloading" them.
More info on UzKart and UzCard can be found (in Russian) here https://gazeta.norma.uz/publish/doc/text97703_uzkart_ot_duet... and here https://uzcard.uz/ru/news/post/uzcard-bankovskaya-tranzaktsi...