What he said. There is no standardized place to hook up an exchange machine. They will hook it up wherever it is easiest to access a line or based on what adaptor fittings they have or don't have. There could be as many as 6-8 possibilities depending on the line and cooler configuration. It sounds like you have the auxillary cooler so if they hooked it up somewhere in that area that makes perfect sense.
And you asked if they would have used a flush or exchange machine. Every "flush" machine I have ever seen is an exchange machine being called by the wrong name. Probably an exchange.

 

However, some dealers and shops will use a cleaning fluid as part of the exchange (this is what is properly called a "flush"), and this is NOT always good. The ones that use BG machines are generally the ones that push this. You really can't go wrong with a simple "exchange" with no additional chemicals.