This is merely my opinion, as I've never come across this issue personally, but I'd be very careful about handing over a mirrored copy of my website before escrow payment is made.

Is there anything about your website that would make transferring it to his web host, complicated (i.e. do you have add'l executables running in the background or anything)?
Have you spoken to him about the details of the current server or web host you're using for your website (i.e. dedicated or shared server, linux or windows hosting, bandwidth needed, etc)? I don't see why he would need to test a full copy of your website, if he has all of the details.

I don't want to say he's being shady, as he may just be legitimately concerned the site will work within the web host/server he's already using, but personally, I would never provide a copy of my website until payment has been made.

Reach out to Flippa about the issue. They may have more experience with this & can provide a solution to satisfy both parties.

Good luck!

Mirroring means your client needs a static version of your site. Normally, CNDs (content deliver networks, such as Akamai) mirrors websites so that content is readily available to the end users without any server-side processing. Its just a simple requirement, do not afraid. Its ok.

If you're using escrow this should be fine. He can't cancel the escrow and he can't steal a site without the domain transfer. Escrow would give you the funds in that case.

According to any escrows services both buyer and seller is protected so don't worry about that.

Make sure he followed the escrow rules and after that proceed to the next steps to website and domain transfer. Thanks :-)