When in Doubt, Consult the Manufacturer
Simpson Strongtie makes it simple, the only fasteners officially approved for use with the product happen to be the ones they make and sell.
From the Strongtie Site:
Attach post to E-Z Spike or E-Z Base with (8) 1/4" Strong-Drive SDS Heavy-Duty Connector screws or 1/4" HDG lag screws and attach post to E-Z Mender using (6) HDG nails or screws per part
Could you use a generic equivalent fastener?
It's pointed out in the comments that Simpson only specifies THEIR screws, but a generic galvanized lag screw ought to work fine. I wouldn't lose a minute's sleep over it. I'd bet there's really nothing unusual about Simpson's screws shaft diameter, material, thread depth, corrosion resistance, etc.
(Goes without saying you have to know what you're doing to substitute; lots of people had decks fall down, sometimes with catastrophic results, because they thought roofing nails were close enough to joist hanger nails. They are not!)
Depending on the locale, code may require that specialty hardware like this be installed according to the manufacturer's instructions. Some products, like joist hanger nails, Simpson's literature specifies generic equivalents; but I didn't see any for these screws. Another hardware manufacturer, they might not make fasteners and might only specify generic hardware for a similar product.
So if you really want to go by the letter of the code, you have to use Simpson's screws. It's not a lot of money and it keeps things simple. I just consider the specialty fasteners part of the cost of the specialty hardware.