2-person mechanics/switching

[Eckley]

I'm a first year official who has officiated more than 20 game so far, mostly using 2-person mechanics. My question has to do with switching. Do the officials switch every time a foul is called? For instance, let's say that A is in the bonus and the Trail calls a foul on Team B. Does the Trail Official report the foul to the table and then switch, going to the baseline to administer the foul shots? I've only had one official insist that this is correct and I was looking for some additional input. It seems like this official may be incorrect. Thanks.