Aion, in its adjective form and in prepositional phrases, can and does sometimes means endlessly ongoing–although it’s a whole other question as to why whatever’s happening would continue without ending. It could only do so by the permission and empowerment of God, so then the question becomes why He wouldn’t put a stop to it.
In the case of Adam and Eve (whatever that story really means), He acted to put a stop to it.
Anyway, speaking as someone who recognizes that the term can refer to endless things depending on context, I’m not worried. It can also (especially in the NT after the development of Platonic thought) refer to something coming uniquely from God. This result is neutral to the question of Christian universalism either way; what matters is whether the term means endless in a particular example, by context, where the established context is hostile to universalism.
This is why opponents try to appeal to parallel term usage in GosMatt 25, for example: these go into eonian life and those into eonian punishment. Other things being equal we would expect the terms to be equivalent in meaning, even though demonstrably (in both the OT and the NT elsewhere) the adjective form can be used twice in close contextual proximity, yet in two different contrasting ways with only superficial resemblance to each other. (The hills might seem to be eonian, but YHWH is truly eonian, for example.)
But if the context of the judgment of the sheep and the goats indicates we should expect a temporary (even if potentially long-running) brisk cleaning rather than a hopelessly endless punishment, then we have reason to interpret the two terms as meaning either two different (though superficially similar) things, or else what they equivalently mean must be something that allows a hopeful result to the punishment.
Note that annihilationists routinely take this route to suggest that eonian means the results of the action will permanently last, not that the action will permanently last. Ironically, they don’t usually notice that universalists also believe the results of eonian {kolasis} will permanently last, however long it takes to get there!–so such an interpretation does not exclude Christian universalism (or even eternal conscious torment, strictly speaking, depending on the mode. For example, God punishes someone once by sending them into a pocket universe prison as punishment and thereafter acts no further in regard to them–but the results of the action last forever.)
Be that as it may. Someone who expects “eon” (or rather a selection of its cognate forms) never to indicate endlessness, will have to take a stab at answering it. I’m not that guy. 
But neither am I worried about it.