You condition any new water, so if you putting IN 1/3 of the water, you condition just that 1/3. However, you can condition the entire tank volume, since it's only 1 gallon it's not going to be much either way so it doesn't matter too much for you
For 1 gallons, yes you should do two 50% changes and one 100% in one week and repeat the following weeks. So it can get sort of stressful after a while, been there done it!
And while we're on the subject, do not use Aquarium salt for weekly use!!!!!!! I know what the package says but do NOT follow it! AQ salt should ONLY be used for medicating sick fish. Too much use of the salt can cause it to be less effective against disease later down the road and can also cause a fishes organs to shut down which equals dead fishie
granted, that won't happen right away but prolonged use of it will. When medicating you can use it safely up to 14 day's but no longer. If you have to keep medicating, give a 5-7 day's of rest of just pure water and continue to treat. But AQ salt should not be used for weekly water changes!