The best advice I received over the years was to make sure that your students get good tone qualities.Concentrate the majority of your time with exercises/long tones/chorales that work on tone quality. Matching Unisons. Then work with the tuner to develop chord/interval recognition.
IN-TONE vs. IN-TUNE
A bad sound will sound out of tune even if the tuner shows it to be correct.
It is easier for students to hear out of tune if all have good sounds.