I am assuming that this diagram is exactly correct. Note the Trans/Ant connections. (Scroll down for text after the diagram.)
You have two SWR meters in series. Each should read the same as the other (within limitations— nothing at an amateur price point is terribly accurate), and neither should affect the other. Lowest reflected power on one meter should also be lowest reflected power on the other.
Tuning for minimum reflected power is mathematically equivalent to lowest SWR.
Assuming your station is exactly configured as shown in the diagram, your problem is one of the weirdest I’ve ever seen. Potentially there’s a ground loop? Does moving cables around change the readings?
My reading of the instruction manual for your transmitter indicates there is no built-in SWR meter. Operationally, I would say to remove the 870 from the system, as it should be redundant.
I suggest taking this up with members of your local ham club, who might be able to see something that’s not visible in the video.