Yup, bad luck. It's why there's always some bargains to be had in December, there's a rush to sell to avoid the next year's tax.
Ironically, the concesionario I bought my new one from, rushed to get the sale through and I collected the car and the temporary "Permiso de Circulacion" on December 28th. The official document came through on January 16th. I went to pay the tax but was told that only the official Permiso counts, so the concesionario is responsible for the tax. Even though the sales document clearly shows I owned it (and was driving it) on Jan 1st! So my guess is that nobody will pay, but if anyone gets chased by the authorities it is the concesionario who is responsible, not me. I even offered to pay, but my Town Hall refused to let me!