It certainly should work and supply 130W, just like TB16 and WD15 docks do over USB-C. Maybe there is a problem with the adaptor or the 9560, try testing separately with other devices.
Btw the 9560 should also work off 60W, but in a restricted-power mode (the CPU downthrottled like on battery, and the GPU downthrottled even more).
I've wondered this myself. I agree with the person above that I would certainly expect the adapter to work at full capacity since the XPS 15 9550 and 9560 both support receiving 130W over USB-C when connected to the WD15 and TB16, but I haven't actually tested the adapter. If it doesn't work, it's probably some annoying firmware bug with the system or USB-PD controller in the adapter, or an issue with the USB Power Delivery negotiation. Maybe those older XPS 15s are programmed to only accept 130W from WD15 and TB16 devices since the 130W USB-C adapter didn't arrive until the 9570 and at the time those systems were created, the only way to get 130W over USB-C (above the official 100W max of the spec) was through those docks. That would be quite unfortunate, though.
Dell xps 15 9560 still have a limit to 90w with an official dell usb-c power adapter. It's impossible to get 130w input. The BIOS is updated. Are you going to fix it? Thank you, Alex.
Can someone from Dell answer whether they will fix this? There's barely an XPS left in existence that hasn't had its charging via charger port completely broken and now they won't even allow us to usb-c charge.
I know this is all by design to get us to buy a new laptop but here's hoping Dell will do the right thing; if they do, maybe I'll consider buying Dell again...