Does the second image now have the white balance As Shot? I believe it must. So the colour and tint 5550K/+49 is the original in-camera setting?
If your source image has the setting "As Shot" and you sync, all your target images should be set to "As Shot". So it will not match colour and tint, it will match the As Shot setting, so each image is reset to how it was in-camera.
If you change your original image to Custom, but leave the colour at 5100K and tint at +23, then sync, all target images will be set to Custom, 5100K and +23.
I've done the following in Adobe camera raw (equivalent to Lightroom Develop module, so likely works the same).
Source Image: Auto white balance, As Shot, 6100K + 2
Target Image: Auto white balance, As Shot, 4950K + 9
Sync #1 - source left on As Shot setting (no changes)
- after sync, target unchanged - still As Shot, 4950K + 9
Sync #2 - source changed to Custom, 6150K + 3
- after sync, target changed to 6150K + 3 to match source (so absolute adjustment made, not relative)
Sync #3 - change Source to "Custom", colour/tint 6100K +2 (same as in-camera)
- after sync, target changed to Custom 6100K + 2
- note that target had no change to colour/tint, values were original
- only change to source was changing As Shot to Custom, and this triggered a change to target
Sync #4 - target was changed to "Cloudy" 6500K + 10 and saved. Source still As Shot.
- target changed back to As Shot
- note that source was completely unchanged, so target changed back to As Shot even though no change to source
So in summary, if source has Custom white balance set, then all target images will be set to match the same colour and tint. But if source is As Shot, then target images will be set to As Shot, meaning they will all have their original as-shot settings which may be different than the source image.