Here is my take at this "USB problem".
First, the noise, as shown, is a typical noise from an on=board DC-DC switcher, with ~400 kHz switch rate, which has no relation to USB signaling. It is very likely that this is an emitted noise from switcher magnetics and/or poorly-designed high-current loops. The noise might be real, or might be just a loop pickup on sloppy scope probe connection, and it might have no effect on actual functionality. Here are some very useful references on ho to deal/avoid switching noise in DC-DC converters, from TI appnote, and from "Power Electronics News"
Why there is no spiky noise when only power is applied? When a USB design is powered up but no D+/D- activity exists, all USB IC fall into "SUSPEND" state by design, and therefore consume little-to-no current. When power consumption is low, modern switchers usually turn into some pseudo-LDO mode, and don't switch. My guess is when D+/D- are connected and all on-board USB ICs wake up due to USB traffic, they begin consuming current, and the switcher starts switching and produces these EMI spikes.
First, you need to check your measurement technique, and use a correct one:
Second, check your on-board switcher if the layout is done in good accord with manufacturer's suggested plan.
Then,... it depends.