Editions: Daedalus Rewards
The Balance wallet in Daedalus Balance Check does not show transaction history which is visible in the same wallet on mainnet in Daedalus wallet.
The snapshot is optimized to bring only the balance of the wallet and not the entire history of the blockchain, which is a substantial amount of data. The only transactions possible in the Balance wallet are the ones that move funds from the genesis block to Balance wallet.
Considering the way that the snapshot works and the intended use of the Balance wallet, which is simply to bring your mainnet balance into the Incentivised testnet and nothing else, you will not have any history for the balance wallet in Daedalus Balance Check.
Note that you will be able to see all the transaction history in the Rewards wallet just like you do on Mainnet for any wallet you have created and used in Daedalus wallet. Balance wallets are different and limited in Daedalus Balance Check.