Does Paypal auto-withdraw from bank?

PayPal automatically draws the money from your check account if that if the funding source. It can take a few days to actually appear on your bank statement and if your account isn't verified it will be sent as an "e check" meaning it will be a pending payment to the seller for a few days so as to make sure the debit to your bank account gets honored ie you have enough money in it to pay. You can also link a credit card and choose which funding source you want to use to pay. If you ever have a balance in PayPal ie a refund or someone sends you money, PayPal always uses any balance held with them first and then debits your nominated funding source for any extra money needed to complete the payment.

You don't have to transfer the money to eBay, but you do need to go to either the email or to eBay and click pay now and authorize the payment.