The Tally algorithm absorbs all this complexity and recommends whatever is in your best interest.
1. With the fact pattern you've provided, there are situations where Tally would only pay the Statement Balance (the smaller amount you mention) so that you can take advantage of your card's grace period.
But if you are not in grace with a card (meaning you haven't paid 100% of your Statement Balances for the previous 2 consecutive statement periods), Tally will suggest paying more/all of the Statement Balance to minimize your interest charges.
Bottom line: Tally is really smart and mathematically suggests whatever is in your best interest.
2. To see if Tally makes sense for you, its a soft pull and then a hard pull to actually open a Tally account.
-Jason (Tally co-founder).