The feat says that "the target must succeed on a Strength saving throw (DC 8 + your proficiency bonus + the ability modifier of the score increased by this feat) or be moved 5 feet toward or away from you."
Case 1: The Push
"But they can't move 5 feet downward from you if they are standing on the ground," you say.
"Ah," I say. "But they can move 5 feet downward from you if they become Prone."
I would contend that this actually fits the RAW as a satisfaction of the requirement "the target must...be moved 5 feet...away from you" as going Prone is a valid form of 5 feet of movement (albeit one that doesn't usually consume any of your Speed). But I can see someone arguing against this reading. Either way, it's a niche enough usage that I think many DMs might choose to allow it.
Extra benefit: If you have the movement available, you could fly down and attack with advantage.
Case 2: The Pull
This is just funny. Let's say you're flying 15 feet off the ground (10 feet above your target). You pull the target 5 feet up with your bonus action, then hit them with an attack. I can't think of a RAW reason this would confer advantage, unless maybe through flanking (if you have an ally who is in one of the 9 squares below your target). But I might rule it granted advantage regardless, because the target would have a hard time defending in midair.
Extra benefit: When the target falls back down, they might re-trigger certain persistent AoE spells or environmental hazards.
Thoughts? Particularly on the application of RAW to force going Prone in Case 1, or to create flanking conditions (or some other form of advantage, if you can think of one) in Case 2?