Dependent care Box 10 - tax due changes depending on answer to "Employer provide care on site" Why?

I have $3000 in box 10 of my W-2 and entered into TurboTax

Here's my question - why does it appear that my tax due changes depending on whether I answer "Yes"  to my employer provides care on site vs. "No" my employer does not provide care on site?

Here my details:

One child (age 12) has $4202 of  qualified summer camp expenses (not at my employer site).  

If I were just to enter this info in, the tax due eventually drops by $1144 (which appears to be ~38% of the $3000).   This appears to be the same regardless of how I answer the above question.

The curious part comes when i enter my second child info.  She was >13 years old, but I still enter her in and enter $0 for qualified expenses.   At this point,  the difference occurs depending on how I answered the above question:

- if I answered 'no', then tax due further drops by $247.   this appears to be 20% of the amount over $3000 ($4202-$3000)

- if I answered 'yes', then tax due drops by $618.   this appears to be 20% of the difference between the two child amount, $6000, and the amount I have in box 10 ($3000).   Even though my expenses were only $4202.

So - -   my employer does provide onsite care, but not for free, and I didn't use it (mine was 3rd party summer camp), but what is the right way to answer the question about providing onsite care?   Regardless, why would the answer to that be impacting the delta in tax due noted above?