Professional company opinion: after you have made sure that your liners are DRY, store them in a cool, dry place (ideally in a boot bag so nothing gets in them) and gently buckled.
If you leave the boots unbuckled, things can break if you are not careful with how you store them (buckles twist, velcro straps get fuzzed out, etc). Also, unbuckled boots will go back to their original mold shape, which means that traditional cuffs would open and then be more difficult to close. That doesn't really affect FTs but when in doubt buckle things up on a gentle setting.