Before add 1099, return is $1850. After add the $4320, it drops to $536. If taxes are around 15.5%, that should mean taxes taken out would be $670. Why drop over $1000

There are many possibilities why this would be correct.  Compare your Form 1040 with and without this income to see the differences in the calculation of your tax liability.

What kind of Form 1099 is this?

(if a 1099-R)  Average 15% is meaningless.  IF your prior income $$ had you already in the 22% tax bracket area...were you under 59.5 when you took the distribution?  then the ~30% assessed = (approx) 22% + 10% penalty  (if no taxes were withheld on the distribution).  OR maybe you were over age 59.5, and were up into the 24% and 32%  brackets already.