But I think it's more helpful to cleanly separate syntax from semantics and instead label the former two as Indikativ I and II, and only then observe that they are used to implement present and past — certain such tenses, and among other things.
If you do this, a lot becomes clearer. The lack of a strong syntactic distinction between the simple and continuous aspects, for instance, is not an issue anymore; it immediately becomes obvious that German expresses the continuous aspect by using optional adverbial markers, or analytically (using auxilliary verbs), e.g. "ich esse gerade" or "ich bin gerade am Essen".
Also, constructs such as futuric present ("ich gehe morgen ins Kino") or futuric past ("war morgen Probe?") cease being paradoxical, since you're not using the present or past tense anymore: you're using the Indikativ I or II, which only usually encode the present or past, and simply don't do so here.
Separating syntax from semantics and thinking about how the former implements the latter rather than directly corresponding to or being identified with it is furthermore helpful for understanding other languages, where the syntax is superficially similar but the implementation of the semantics differs from what you're used to.