iirc they need proof of insurance to tax a vehicle for you.
You need to either A) bring your insurance certificate in for them to tax it (had to do this when i bought a citroen) or B) you take them up on their offer of free 7 day insurance and they can use that to tax it ( did this with my VXR)
Either that or they sell it still with Tax on, as happened with the Volvo which still had 8 months tax.
But as fox says, they won't pay to tax it, if it runs out during their possession of the vehicle. If you expect tax when buying it, it should be discussed so you can bring in your insurance, never assume they will automatically tax it for you.