I'd always cure outside the tank, esp a new one. Al that die off the ends up feeding your cycle all ends up as nitrates in your new tank not to mention what ever else decays off of it. I'm a believer that all the good bacteria that I need will be on the LR
after the rock gets cured. So by curing outside I don't have to gunk up my new tank, deal with the nitrates or do massive water changes to get the nitrates (and smell) down.
Instead I cure in a tub, do minimal water changes there. When the rock is ready, 1,2,3 plop plop into the display/sump and let the bacteria take hold where ever else it likes. Feed ammonia for a day or 2 to make sure then it's fish time.
That way my display starts out at 0 ammonia, o nitrite/ 0 nitrate
and the tub I just rinse and store. Most important the cycle would be with tap while my display is ro