no it is not tied to the framerate. I changed the framerate of the UI files to 60fps, so they just run faster and thus appear and feel smother, no matter which framerate your games is running at :)
You can find compatibility patches for various mods (including SkyUI) in the files section. Just download them and pick the patches you need out of that file :D
I know this has not been updated in a while but in case the author still cares, a compatibility patch for SkyHUD would be great. https://www.nexusmods.com/skyrim/mods/87259
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60 ui obsolete - book, bookmenu, fadermenu, giftmenu, levelupmenu, lockpickingmenu, sharedcomponents, sleepwaitmenu, titles, widgetoverlay
I got mine from here: https://forums.nexusmods.com/index.php?/topic/955584-fffffff-perk-names/
https://www.nexusmods.com/skyrim/mods/87259