If the tax was paid in 2018, and it was owed in 2018, then it is deductible in 2018, regardless of how long it took the state to process the payment.
EDITED 1-15-2019 2:52 PM (CST) to add section below:
The vehicle registration is deductible only if it is a tax. It has to be based on the value on the vehicle. Some states only part of it is deductible as some have a flat fee plus part is based on the value.
See below for more detail on your respective state.
https://ttlc.intuit.com/replies/6145391
