Yes I see what you mean. Regarding the frequency response, there is no problem. There are no any bumps or conflicts on the split points.
But the problem is the delay. You can see it in the phase diagram on the video. The wave look (similar to saw tooth) in the above video indicates the delay (a couple of milliseconds). Normally the phase diagram shouldn't look like that. It should look like almost a flat line.
Look at the below multi band compressor plugin. When the crossover frequencies are changed, there is no shifts like that. The wave shift is in the end of the line but it has so small interval. Also no change at all, even the frequencies are changed.
Normally, band splits don't cause any delay issues (causes phase issue). You can try any band split plugin.
NOTE: The phase diagram is
Inverted Raw Audio Signal
Processed Audio Signal. The ideal should be a flat line. This is also called Null Test. Because if there is no delay, the signals neutralize (null) each other. The bump on the low frequencies in the below video is because of the high pass filter in the plugin, that's normal.