Why did I get charged $127.14 without any email warning?

Check again ... check your spam ... you should have gotten at least 4 email alerts ... this is why your email address is confirmed before you file. 

Were the fees supposed to come out of your refund?

If the IRS is taking too long to send your refund you still have to pay the fees in time.

See What if the IRS reduces your refund or delays it.

https://ttlc.intuit.com/community/payments/help/what-if-my-federal-refund-isn-t-enough-to-cover-my-t...

Then when the IRS does send your refund they won't take the fees out again.

And, Why you got charged,

https://ttlc.intuit.com/community/charges-and-fees/help/why-was-my-bank-account-auto-debited-for-tur...

You should have received about 4 emails asking for the fees.  If you don't pay as directed when directed  they will debit your account as they already have... you agreed to this when you signed the contract (not once but twice).