WoW - you tasted the water, that can't be good.
First off congrats on your new puffer. Awesome choice. I have 2 adults in a 30gl tank myself.
Here are some pointers and questions that should help you. PH is fine (7.6-8.2) and so is your temp (72-82*F), nitrate within range (less than 30 ppm). My first question, has your tank been cycled yet? If not you should help that along as soon as possible. Puffers are very sensitive to ammonia and nitrite. Both should remain 0, though you well have bumps now and again, "water changes, water changes, water changes" that's the key.
Now your salinity issue. I'm a little confused about your hydrometer "calculate 24hrs" must be a classy one. You should also get one that gives you an instant reading, for example a floating one. That type of hydrometer is cheap, quick and perfect for use in a 5gl bucket you can use for water changes. However your salinity level well likely end up being just fine.
My personal beliefs are this:
very young*= 1.000-1.002 *meaning after birth + shipping
young*= 1.002-1.006 *day you brought home -3 months
adolescent 1*= 1.006-1.010 *3-6 months
adolescent 2*= 1.010-1.014 *6 months-1 year
adolescent 3*= 1.014-1.018 *1-2 years
adult*= 1.018-full marine *2 years +
I also strongly believe in fluctuating the salinity within the settings to imitate the wild. Now these are just my personal beliefs based on years of experience. These are in no way "the rules". And yes you need marine salt such as Instant Ocean.
More misalanious tips:
*must feed snails to them to keep teeth trimmed
*puffers are carnivores so feed them meaty foods frozen and/or live
*vacuum substrate during every water change
*move decor around during every water change to imitate wild (puffers are also very curious and like to buzz around
searching new scenery)
*puffers do like to lay around on the substrate especially when no one is in the room to watch them
*do not make them puff up
*very aggressive fish well not tolerate very many tank mates I recommend keeping it in a species tank
*If your going to keep more than one, get them now so they can grow together
*puffer also change colors don't worry it's normal, although a white belly is a happy fish
*if tail is curled tightly to side it's stressed and or scared
*although prolonged dark belly, curled tail and sitting on the bottom indicates that something is wrong (water? or illness?)
If you have any other questions just ask.