If you upgrade to a paid account before the 60-day trial period ends, any remaining portion of your initial $300 credit remains in your account. This credit expires after 60 days, when your free trial period would have originally ended. Any charges you incur between your upgrade and the expiration of the free-trial credit are billed first against the credit.
When your free trial ends, your account is paused. Your credit card is not charged unless you upgrade to a paid account.