"My understanding of Estimated Payments is that based on current year's income, you should estimate next year's estimated tax. "
Yes, sorta i guess. I think that applies to people who use the "safe-harbor rule" which i do. Personally, i estimate my tax liability for the whole year (2024 in this case) as same as my tax liability for the previous year (2023) and divide it by two and send the IRS the payments in Quarters 1 and 2 of 2024. So i front-load the payments, to be safe, because it matters when you pay your estimated tax. But the safe-harbor rule doesn't work for everyone. It sounds like you just had a job pop up in October 2023 and got paid then. The IRS knew about it because they saw your 1099 but the Turbotax program needs to be told when you earned the extra income otherwise it'll default to all four quarters. You would've been OK if you made an estimated tax payment (1040-ES) for the 4th quarter (i think it would've been due Jan 15, 2024) because you had earned it in the 4th quarter. If you had earned it in the 1st quarter of 2023, the Turbotax program would've been right to penalize for all 4 quarters.
