Conditional rendering in a popup only works if the model of the rendering condition is the same model as that of the model of the "context" that opened the popup. (i.e. The model of the page title of the button that opened the popup or the model of the table that popup is a row action of).
I did some further testing and realized that this issue only occurs in a very specific situation.
It appears that it occurs only when both models share the same sObject and the (model) field value of the rendering condition is changed after the popup is rendered, in which case the new (changed) value of the field has no effect on the rendering of the component.