Escrow does not ever pay the property taxes. Rather escrow always uses the assessed value on record at the county, and will prorate the closing statements for the buyer and seller accordingly in the forms of debits or credits.
This can be problematic because when you get your bill in April, that assessed value will not correlate to the prorations that escrow calculated because they use whatever is on record.
This makes it tough for escrow companies to give definitive answers when assessed values are in a state of greater flux. We run into these sorts of problems alot because of the flips we do. Since escrow only credits/debits the buyer and seller, in one case we had a fairly large discrepancy in one of our transactions. In essence we had escrow write a letter to the buyer and the buyer actually sent the difference back to escrow that then conveyed to us as sellers.
In your case it is you the buyer but the same problem still exists. Now the county will most likely send you the second installment since it occurs in a few days but not late til 4/10 and it should be the same as the first installment which is what escrow has on record. You will then get a supplement which should be some sort of refund but… you never know.
