Starting interval running (HIIT). Does that conflict with weights?

Male, 32, 175p

I've been running 3/week (6k-10k) and doing core/bodyweight exercises 3/week. I've switched from steadystate running to bursts, starting with (1 min sprint/3 min walk) x 6. I'll decrease the rest and play with the number of intervals as I improve/get bored.

Three days I week I do pullups, dips, core work, and a little bit of leg work (1-leg squats, ham lifts) for 45 minutes.

My question is: The literature on HIIT seems to suggest that there should be no extra distance or leg work. Am I negating the the benefits of HIIT by doing off-day workouts?