Internal SWR meters are notoriously inaccurate. They are no substitute for a GOOD, external power/SWR meter.
Especially if you already own the meter...
VA3BPO, there are actually things you can learn by putting certain SWR/power meters in between the tuner and antenna, but the things you can learn there are a bit academic. In other words, not anything that's going to help you get on the air, just things that can help you learn about transmission line theory. So you maybe want to save such experimentation for later. Plus, putting it between tuner and antenna, aside from not quite telling you what you want to know without some subtle interpretation, puts some significant stress on the meter because the voltages and currents are higher than what it would see in normal service in a matched feedline.
So when you want to make sure your tuner is adjusting itself to present a good match to your radio, the salesman gave you the right advice: SWR/power meter goes between the rig and the tuner.
Don't put it in the closet