The Repelling Blast Invocation applies to each hit

Since we know you can select the target of each separate Eldritch Blast ray separately , even to the extent that other Repelling Blasts could actually push the same creature out of range of the remaining subsequent beams, we must rule that Eldritch Blast (no matter what Invocation is attached to it) is a single spell that hits in sequence, not simultaneously as per Magic Missile.

This is further expanded upon when we look at Hex, which triggers each time an attack hits the Hex'd target.

So the only conclusion the sound logic and readings of these rules can give us is that Eldritch Blast, Scorching Ray, and similar spells that require multiple attack rolls to hit their target(s) are NOT simultaneous and always hit independently of each other, in succession, unless otherwise noted in the spell's description.

As you pointed out, the prerequisite for Repelling Blast is:

"...When you hit a creature with eldritch blast..."

Eldritch Blast requires you to determine if you hit or miss each target or targets for each beam (not once per spell), thus letting us know if the requirements 'when you hit' or met or not. Repelling Blast, and any other feature, trait, spell, or spell-like ability that activates when hit or attacked by something would trigger for each Eldritch Blast beam.

So yes, at 5th level with 2 beams you could push a single goblin up to 20ft away, or push 2 different goblins up to 10ft away from you in a straight line. You do not need a separate ruling for hitting the same creature with multiple beams, because your ruling is already included in the spells text.

It's going to be up to your DM

This is definitely an edge-case - and even moreso because it's language used in Unearthed Arcana which Jeremy Crawford has stated that:

Unearthed Arcana material isn't tuned for multiclassing. We make a class/subclass multiclass-ready if it's going to become official.

Odd interactions like your question are bound to come up and will likely be dependent on tables as to how to adjudicate if multiclassing is pursued.

A reasonable approach

Having said that, it does seem like the two abilities should interact. The requirement for the curse is movement due to casting a spell, which is exactly what is happening with Eldritch Blast with Repelling Blast.

Your DM may initially allow it because of...logic :) But table experience may determine if the combo is overpowered or not. If so, don't be discouraged if they want to roll back the allowance and bar the interaction.

Multiple Blasts Concern

As Ben Barden pointed out, EB provides more than one blast. No other sorcerer cantrip that delivers cold, lightning, or forced movement does this. This is another interaction unplanned with the UA multiclassing.

Once again, it's up to the DM how they want to handle the curse application here. But given a successful series of hits could then push the target back in multiples of 15, this suggests a problem with the interaction and a reason not to allow it. However, if they decide "that's awesome!" and it works for them and the table - then allowing it is reasonable as well :)