Ok it looks like your settings are correct. Thanks for providing this example, but I’m sorry to say its difficult for me to tell what is going on in this video because there is no metronome and your drum track has a heavy swing. A simple way to test this would be to loop a single snare drum hit that plays in time with an audible metronome, so if there is an issue with latency it will be easy to see/hear it.
When I use Logic’s native bypass, there will be a small stutter because Logic is calculating the latency with the plug-in on/off, but this corrects itself very quickly. If you use SplitEQ’s built in bypass, you won’t experience this stutter because the latency isn’t changing. If you’re not experiencing latency issues when SplitEQ is active, then I would suggest using SplitEQ’s built in bypass.