Transaction Issue

That would depend on how each of these entries is categorized. A correctly categorized transfer in the savings account would use Category = [checking account] (name of checking account in [square brackets]). This automatically creates a linked transfer transaction in the checking account. When switching to the checking account, you need to match the downloaded transaction to the just created transfer transaction. Anything else and you may end up with a duplicate register transaction which is un- or mis-categorized.

IMHO, for best results manually enter transfer transactions into your register BEFORE you download transactions from the bank which contain the transfer confirmations. For recurring transfers use scheduled reminders and enter them a day or two before the due date. Be sure to use distinct Payee Names for each transfer / credit card payment to avoid confusing Quicken - memorized payee entries.
That takes the guesswork out of the download process. Because a correctly entered transfer transaction already exists in your account registers, the process should just match the downloaded transfer transaction to the existing one in both accounts.