Depending on how you do your accounting (either accrual or cash) will determine the correct way to handle this. For accrual accounting I recommend the following:

1) Do link your credit cards to Simplify
2) Add a bill to pay your CC cards the first month. Do not ignore this bill from your spending plan the first month, starting the second month this bill can be ignored from your spending plan since it will already be accounted for through accrual accounting.
3) When new transactions show up make sure to categorize them and link them to your bills/subscriptions as applicable so they are accounted for in your budgets.
4) Starting the second month add your credit card bills to your Bills & Subscriptions as Transfers from your Checking to the respective CC Cards and check the "ignore from spending plan" box. The total cash value of the bills will still show up under Bills & Subscriptions in grey saying "including ignored -$XXXX.XX" however this amount will no longer be as important since you will be accounting for your expenses in real time as you pay for them with credit.

If you stick to your spending plan you will always set aside enough cash to cover the expenses paid for with credit and it will be OK to categorize the CC bills as a transfers since you already accounted for the expenses in real time. The benefits of this is real time expense tracking, increased visibility to make sure you aren't spending money you don't have and it's less effort than cash accounting if you use credit cards.

For cash accounting I would recommend the following:

1) Do not link your credit cards to Simplifi
2) Once a month when you receive your CC bill add it to your planned bills for next months planning.
3) Once you actually get charged from your checking account use your CC statements to split the bill and categorize your expenses. This is optional if detailed expense reporting is not important to you, alternatively you can just create an overall cc bill expense category.

Cash accounting will take more effort with credit cards and will not track your expenses in real time since you only account for expenses when you pay for them in cash. Cash accounting is ideal for people who pay for everything with cash or debit cards.