Keeping those "tabs" sticking up helps in putting on, adjusting, and then taking off the boots. With the tabs up, it's easier to find the slits to stuff the lacings through, when you tie it all up it's much like the tabs on a drum, you can adjust the "tension" by pulling the tabs about to get a more snug fit (or loosen it) and then take up that slack with the knot at the top/end. And when you take them off, you just undo the knot and then pull apart each pair of tabs until you can take off the boot.
I've also found it more comfortable to have the tabs up anyway, if you have them flat, they tend to dig into your feet and just sit uncomfortably, as well as always wiggling out of adjustment when you walk around, when the tabs are up there is much less chance for that, they appear to be more flexible but still secure when the tabs are up.
I've also noticed that when you have them laced [tabs up], if someone steps on your heel (or stumbling on yourself...admit it!) the boot stays securely on your feet. When wearing sneakers, it's easy to have it come undone or just pulled off your foot when that happens.
Now, actually lacing them up, I'd say that's up to the individual. Do what works for you.
Andy Volpe
"Build a time machine, it would make this [hobby] a lot easier."
https://www.facebook.com/LegionIIICyr/
Legion III Cyrenaica ~ New England U.S.
Higgins Armory Museum 1931-2013 (worked there 2001-2013)
(Collection moved to Worcester Art Museum)