Most jig hooks have the eye upwards, meaning it will always swim with the hook pointing up. I haven't seen ESA using it down ( Must say that I don't always watch ESA) but know that you can rig it as you want. I have rigged it with the back up, Belly up and even side up and had strikes on all those methods. What I did find critical is that the dropshot must not spin. I caught fish even when it did, but got more strikes the same day when it didn't. My advise, rather look at things such as the:
1- Tide (In most cases the incoming to high tide is the best to fish)
2- Time of day (most species are active all day, but it proved that early morning and late afternoon has produced a lot more aggressive strikes)
3- Water visibility (in my personal experience I found that the cleaner the water, the faster the retrieve, Clear and white dropshots seems to me the favourites, that is if you target game fish species. I also got some nice game fish species such as bump nose kingfish, salids and shrimp scad in murky to dirty water going at a slower retrieve. In these cases a darker colour worked better.)
4- Area (Be sure that you get to know the areas you fish in. it is no use fishing a area where even bait fishing is bad. River mouths or rocky areas in estuaries seems to produce a lot of species.
5- Water temperature (This has also made a difference in my fishing. I find that the fish mostly bite better in warmer water. The fish is active and aggressive in these conditions. If the water is cold, try to go slower and lower, go down to the bottom if you have to and I'm sure you'll get something.)
Just try and see what works best for you
Good luck and tight lines :fishn