This has been reported elsewhere for earlier versions. But I’ve been trying this with our installed version (3.2.4), the latest downloadable version from webix (5.4.5), and the latest version in your demo area. (https://webix.com/demos/scheduler.html) currently running 5.4.6. They all have the same problem:
Open the Scheduler calendar using iOS device and click the next/previous buttons once. It consistently moves two days instead of one, and two weeks instead of one. For some reason, month view seems OK.
We’ve also wired a custom function to the Add Event button, and that’s run twice also.
I’ve tried this using Safari & Chrome (69.03497.105) on iOS 11.3.1 on an iPad. I’ve had the same reports from iPhone users.