D&D 5E Do Push effects work on ( thus dismount ) riders?

[miniaturehoarder]

Just curious about this one. Do Push effects work on ( thus dismount ) riders? Mount rules are kinda light and was wondering on other folk's opinions.

Edit: The Basic rules and PHB account for the mount being pushed and proned, and the rider being proned, yet the rider getting pushed was a matter the rules were silent on.

If an effect moves your mount against its will while
you’re on it, you must succeed on a DC 10 Dexterity
saving throw or fall off the mount, landing prone in a
space within 5 feet of it. If you’re knocked prone while
mounted, you must make the same saving throw.

If your mount is knocked prone, you can use your
reaction to dismount it as it falls and land on your feet.
Otherwise, you are dismounted and fall prone in a
space within 5 feet it.

 

[Sunseeker]

I think it's implied in the last line of "if you are knocked prone..." also includes "if you are pushed" and I would say that KISS applies the same DC to such a situation.