I think you’re correct in your understanding, and I poked around because your pictures and description made me wonder about the power adapter and the cables. Based on what I’m seeing online, the cables are connected correctly: In this image of your PoE adapter, the yellow cable to your Ubiquiti NanoStation is plugged into the adapter’s PoE port, and the white cable to your TRENDnet wireless access point is plugged into the adapter’s LAN port.
In a Quick Start Guide I found, I noticed that it says you should be using shielded cables for your Ethernet connections. I can’t really tell about the yellow cable, but the jacket on the white cable appears to say “UTP”, which indicates “unshielded twisted pair”. I wonder if using different cables would improve your situation, especially with so much metal around. I don’t know if it would or not, and I tend to agree with @dave27’s assessment, particularly regarding the signal LEDs that indicate signal strength to the NanoStation in your shop (but looking at the lights I’m also wondering why the power and LAN LEDs aren’t green; maybe that’s just lighting in the room).