Assuming it's torqued to spec, pop the cassette back off, grease the Driver threads, and rotate the cassette around on the freehub body until it feels like it has seated fully. Then tighten the cassette back onto the driver and your problem should be gone.
The XD Driver doesn't use any spacers because it was designed for a few specific parts without a large range of adaptability, so you're not missing spacers or anything like that
If both cassettes wobble, gotta be something with the axle/body. I'd pull it all apart and check for a bent axle or something? Any shims or spacers in the body? I vaguely remember one of my xD wheelset, the driver body had two shims/spacers on each end that the axle went through. All of my wheels are a bit different so there doesn't seem to be too much of a standard to pinpoint an issue.
If you've got the freehub off: place the wheel in a place where it won't move (hole for the axle in a work bench?), and check the axle with reference to the hub bearing using a small straightedge.
That said DT hubs don't work well [read: at all] with a broken axle, so check the dumb stuff: ratchets have no damage/contamination, the sliding keys are clear of debris, and the springs are not damaged.