Other banks certainly don't have automatic transfer, and there must be a handling fee, and the transfer must be more than 5 days in advance. You can transfer money through ICBC's online banking.

Why don't you get a debit card from China Construction Bank? Can't you tie your credit card to your own name and repay it yourself?

I use China Merchants Bank's credit card, which is self-service repayment every month. It's convenient. I don't have to worry about it at all.