When transferring coins / tokens over bridges, you need to make sure that you can access the used account address on the recipient blockchain. The simplest way is by using wallets which support both chains, so that you can see the token on the other chain right away. Recommended wallets are:
You have to send your ATS coins via a mediator contract to the xDai Chain and there you will get the xATS_tmp (ERC20) tokens. This xATS_tmp tokens will be received on the same address on the xDai Chain.
Send the desired ATS coin amount to the mediator contract at:
On the xDai Chain you receive xATS_tmp token in the same amount as you have sent to the mediator contract.
In Alphawallet you should see the xATS_tmp token automatically, but for Metamask and MyCrypto you will have to add the token to make it visible in your wallet.
The xATS_tmp token contract address to add the token to the wallet is:
The xATS_tmp token contract can be found via the xDai Chain blockchain explorer (here).
Additionally every account will get 0.01 xDai to pay for transaction fees.