This device doesn’t change the functionality of your Digitakt.
It won’t give your Digitakt direct jump. It won’t make your Digitakt change to a new pattern in the middle of a playing pattern.
Those videos show your follow actions flipping through clips within a beat or so. Is your pattern on the Digitakt 1 beat long? If not, it won’t work. You need to have your clip changes quantized to change at the same length of the playing pattern on the Digitakt. Your next clip will arm just before the pattern on the Digitakt finishes, giving it time to change to the next pattern right as the next clip starts playing.
Pattern clips simply sends a program change when you arm a new clip to play. You still have to time your clips to change near the end of a pattern.
Normally sending a program change right when your new Ableton clip starts playing isn’t fast enough to have the pattern change until it has played one more time. This device makes it so it sends when you arm the clip, rather than when it starts playing.
The first issue you’re seeing where you start and it misses the first clip is because the clip is never “armed” to play. The clip just starts playing because the transport is stopped. When you start from stopped you need to have the pattern set to whatever pattern you want to start on.
Try something more simple to start.
Use the default clip settings and patterns that are only 16 beats long on your Digitakt. Click on the next clip or scene just before your Digitakt pattern is going to loop around to the beginning again. If that works for you, then you can start trying to make more complex changes. Just be aware of your pattern length on your Digitakt and set your clips quantized to change accordingly.