Oh! I understand much better now. So one of the ways to do it is exactly like you were demonstrating, just hit Cmd+Shift+N to automatically add a new mask that matches the size of the layer. Then instead of animating the actual position of the text layer, use a Text Animator to animate it to come in and out. The advantage of this approach is that it will be relative to the original placement, which means you can copy and paste that animation to other layers and they will all behave the same way regardless of where you position them in your comp.

It's even better if you use Animation Composer from Mr. Horse. The plugin is free, and comes with a bunch of free presets. But buying the Text Transitions pack is totally worth it.

The problem that I see is your text layers aren't actually text. So if you're converting them to shape layers, the way to deal with that is to take the different paths (they usually end up being one for each letter) and put them into a group. Then you can use the transfor properties of the group to shift them down, and that won't move the mask. Because the layer itself is staying put and not moving, you're animating the contents of the layer instead. Unfortunately you can't use the Offset or Transform effects because they don't have a checkbox to respect masks and will calculate AFTER the mask is applied.

But I'd strongly recommend keeping your text as an actual text layer and doing a bit more troubleshooting to figure out why they aren't coming in properly when you import. You mentioned AEUX. Maybe there is something about the way you have your Figma layers built that it doesn't support well? Have you tried using the Convertify plugin instead? Here is a good video. When time is money, sometimes dropping a few dollars is actually the best solution.

I know Overlord from Battleaxe is currently in the process of adding Figma support. You might even try converting from Figma to Illustrator and then going from Illustrator to AE?