4 weeks is just an estimated time for kilning, some strains require more time, I generally go a week or two after the smell of ammonia has gone, but that's just me - usually not rushed to smoke.
After kilning, tobacco seems to benefit greatly from a resting period. Sometimes, I'll blend & shred straight from the kiln, then pack in bags or containers to rest for whenever I'm ready to smoke. For me, the resting period is only a few weeks, but may be months or years.
I use my kiln to flue-cure the bright leaf strains first, as they come out of the tobacco patch, then de-rib and store in low-case until the other strains have been fully air/sun-cured, kilned and de-ribbed. Then, blend & pack away in Don's bags until I shred. To me, shredding is a PITA with my hand-crank shredder, so, usually not done until needed or nothing else to do - need to spend the $$$ for a motor-powered shredder.
My 2019 & 2020 crops were a bust, damn-little usable tobacco (long story for another time). But I had some 2009 burley & 2011 bright leaf, both air-cured, that were really harsh at the time, stored away, but now decent. Blended with what I had, got a decent smoke - but still had to buy some tobacco from WLT.
Do they need to be low case before shredding?
Keep in low-case for resting-period or storage, to insure mold is not a problem. Caution - some heavier leaf may initially seem surface dry be still contain a lot of moisture - pack away, but check every couple days, until uniformly dry-case.
I bring my tobacco up to medium-case in my kiln, for shredding. Low-case seems to produce too much crumbs or powder.
After shredding, I spread out the tobacco in a large tray, toss/fluff/mix, to dry back down to low case before packing away.
If I'm not careful about this, I have mold problems.
I prefer my tobacco somewhere between low to medium case for rolling cigs, so, will bring moisture back up when I roll.