Here's another way to think about it.
The "Dual-Wielder" Wielder" feat only removes the "light" requirement from the wielded weapons. You still need to take the attackAttack action, and that attack must come from a weapon held in one hand. Effectively, it modifies the two-weapon fighting rules as follows:
When you take the Attack action and attack with a
lightmelee weapon that you’re holding in one hand, you can use a bonus action to attack with a differentlightmelee weapon that you’re holding in the other hand.
Emphasis mine.
Two-weapon fighting + Dual Wielder doesn't care about weapon properties at all. If you, for example, somehow gain the ability to wield and attack with Greatsword one-handedly, it would also be viable for use with your Dual Wielder-enhanced two-weapon fighting.
In short, Versatile weapons are totally valid to be used with the Dual Wielder feat (though, since you're wielding it one hand, you'll never benefit from the Versatile property itself). As long as you can attack with the weapon (and one-handed one-hand-wielded Versatile weapons fit the bill), it's valid thanks to Dual Wielder.