I tested it and it did not appear on the D-6's Bluetooth mode, I tried AppleMuisc and Spotify and neither felt the lag to when cutting songs.I recorded a video, so maybe I can show it sometime.Are you able to test Bluetooth on it and check whether if there's a second or so starting lag when playing an audio stream on the transmit side?
Its happens on the DO100 and its annoying enough that I swapped back to the Topping D50s for speakers on Bluetooth duty.
The only thing I found that had an impact here was download speed/download response, AppleMusic I chose Hi-Res Lossless, and while Bluetooth mode doesn't push with it, it needs to download Hi-Res Lossless/Lossless to this device to buffer it a bit before pushing the stream, on some songs, especially in less CDN friendly regions, there may be a hint of loading lag, which is not encountered on Spotify.