Most webhosts probably would not allow you to install Phalcon, shared hostings aren't good options for high-traffic websites, you can ask them about that or try any of these hosting providers: https://phalcon.io/en/hosting
Sometimes hosts allow you to do that (ie, Site5) but I guess you will have to ask the tech support first if this is supported at all (they will tell you to use either a custom php.ini or rebuild the PHP).
But yes, I would suggest to order a VPS or a dedicated server — this is usually a much better option.
Even if he goes with a VPS or Dedicated. If he gets cPanel it does not support Perl Threads to install Phalcon. So I would make sure with the hosting company before you spend your money on VPS or Dedicated.
I asked my existing host, so no..so I there would be another hit on my wallet :) pretty soon, but I'll try it on dev VM's as I seriously wanted to benchmark those request/per sec of Phalcon..to see if it'll go in my next mobile API