Hey Esteban! Sorry for the late response.

They main criteria when selecting predictors is they should be independent of the intervention. So, any variables that are lagged to the pre-intervention time window are fine because they can't be impacted by the intervention (by definition). For predictors with values during/after the treatment, they should be exogenous of the treatment.

From what I've seen, defining independence is more of a subject matter call than a statistical one. You could throw a statistical test at it, but I would argue that indepdence from a conceptual standpoint is more important.

Great question! And if you've found any good resources in the meantime, I'd love to hear.