Learn Spanish (Latin America): Nosotros trasplantamos el árbol después de que él comprara la arcilla. - We transplanted the tree after he bought the clay.

This highlights the Latin American variation you are currently learning. Traditionally, después de que followed by a completed past action takes the indicative (like compró). However, in Latin America, it is extremely common to use the imperfect subjunctive (comprara) for these completed past events instead.

Could we just say después de comprar instead of después de que él comprara?

Not in this sentence, because there are two different subjects. "We" (nosotros) transplanted the tree, but "he" (él) bought the clay. You only drop the que and use the infinitive (like después de comprar) when the same person performs both actions.

How can we tell if trasplantamos is in the present or the past tense here?

For regular -ar verbs, the nosotros form is exactly the same in both the present and the preterite (past) tense. We know it means "we transplanted" (past) rather than "we transplant" (present) because the other half of the sentence is anchored in the past with the imperfect subjunctive (comprara).

Since después de que allows this regional variation, does antes de que also give us a choice between the indicative and subjunctive?