I use kettlebells in my HIIT workouts, not as strength. Sometimes I do entire kettlebell workouts, with deadlifts and get ups and presses and sometimes the swings are just part of my normal workouts. I will also use the kettlebell instead of dumbbells for squats and lunges too. When I set up a HIIT/tabata workout, I try to hit legs, core and something for my arms/shoulders and get at least one high heart rate item in there like burpees/mountain climbers/jumping jacks. Mine are typical 5 exercises/4 rounds of 50 sec work / 10 sec rest for a 20 minute set.
I think of lifting heavy things more as single efforts that just focus on weight lifted rather than the speed it's lifted at... more along the lines of "get this tree trunk off of my baby!" or "move these boulders out of the cave entrance," or "haul this antelope carcass home." Kettlebell swings are about being fast and explosive, more like throwing spears or something. :)
Without any other variables such as your body weight or fitness level I would respond purely based on the amount of work you are doing and the primary energy system you are using to accomplish the work. Six minutes of tabata style intervals with a 25 lb. kettlebell would put you towards the aerobic end of the anaerobic/aerobic pathway.
I typically throw in this type of conditioning work after a more traditional strength workout: basic lifts, heavy weight, low reps (3-5), plenty or rest between sets.
Personally, I'd up the weight and lower the time(due to exhaustion). Keep moving the weight up as your capable of finishing more reps. Strength gains will be faster and so will endurance. I put on muscle super fast by exhausting with the heaviest things I could find once every 5 days, then feasting after.