Well, this is completely debateable from a few different views. However, I'll just give mine
First, it depends on the age. My own children (3, 5, and even the 8 year old) make grammar mistakes when speaking. "I'm be carefuling." So to some extent expecting high levels of accuracy might be a lofty goal (depends on students age, I guess.) My kids speak like native speakers but they have little English input outside of the home.
However, with my students I feel they have 'got it' when they can switch between tenses as needed. That takes them 4-6 years. (I see them as a group, once a week for an hour.) Also, I'm talking about speaking in the flow of conversation, not a testing environment. One thing to be careful of is that of course they can answer with the form they've been practicing recently, that doesn't mean they understand the grammar, though.
I generally stick with one tense for maybe a year or so. I of course teach other things and present tense with 'be', 'like', 'want', 'have' and other stative verbs are ubiquitous throughout my curriculum. I'm talking more about actual conjugation and work with the time-ense relationship.
I start with present continuous, then past, future, and finally present. Actually, I spend a long time on the first 2 and then the last 2 are quite easy to grasp once they understand the whole idea of tense and time.
I don't do any explaining in L1 until they are near the end of 4 years and at least 10-11 years old. Children don't get that kind of grammar explanation in schools until 5-6 grade, if that. Here in Japan, kids learn grammar terms and such in English class (7th grade). So, even if you say "this is a verb" in their L1, they don't know what a "verb" is.
If they are older and you are teaching "the mathematics" of conjugation then maybe you can move on. By "the mathematics", I mean the equation "be"+ ~ing. With older students and adults this is easy to understand because they understand grammar in their own language, ie the tense-time relationship.
I always err towards better to practice one thing a hunderd times than a hundred things one time.
I've started rambling ... Again, there is no correct answer as far as I know, but I'd say if your students aren't struggling with formation or understanding, then you can move on. Yet, there's nothing wrong with more practice and solidifying a foundation before moving on.