If you are able to personally identify something in Analytics using your user ID, you will want to 'pseudonymize' it.
Typically a client-side implementation firing a purchase event on the thank you page is enough to see conversion for a given visitor. However, if you want to see as accurate data as possible, you can explore the possibility of implementing something server-side on your backend servers that would send data to Adobe Analytics on a successful purchase. This is not an easy or simple implementation, and quite honestly is likely more trouble than its worth.
If I am correct using POST or GET you need to provide <visitorid>, <mcid> or <ipaddress>. If I use the (the client's) customer ID for the <visitorid>-field and use customer ID in the right eVar field I should be able to connect the "purchase", however during the client-side process Adobe reports on visitorId or MCID and not on the client's customer ID. So, for Adobe Analytics I have two different visitorIDs for the same customer ID. Is this assumption correct?
If you wanted to make the purchase event seamless with the rest of the customer's visit, you would want to make sure the visitor ID or MCID matched the value stored in the Analytics cookie (which one you use would depend on which one is currently being used in your implementation). This means you would want to pass that cookie value to your server, so the server can send the image request to Adobe's data collection servers.