Originally Posted by SDPhantom
Ticks do change based on spell used, but the number of ticks always remains the same for the same given spell. For example, no matter how much haste a warlock has, their Rain of Fire will always have 4 ticks as long as they aren't being hit with anything. Pushback from damage shortens a channeled spell's cast time, therefore reduces the number of ticks the spell gives. Haste only scales the entire thing as a whole, shorter tick delays and shorter cast time.
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Some spells gain additional ticks from haste, others do not. E.g. Divine Hymn, Hymn of Hope and Drain Soul gain ticks, Mind Flay and Mind Sear don't.
Pushback shortens channels, but does not always cut the last tick (though it does most of the time). I'm completely unaware how this mechanic currently works.