Well dissolved solids can be a little complicated, but water hardness makes up a lot of Total Dissolved Solids. Its basically how much stuff is dissolved in the water. Hardness is how much of a particular stuff is dissolved depending on what type of water hardness you are testing for.
If the fishstores you are buying from has particularly hard water (lots of dissolved stuff) and you have very soft water (not very much dissolved stuff) the sudden change in water type might not be good for your fish. There are tests for this.
It sounds like you are just temperature acclimating. You could try slowly mixing tank water with the water in the bag so the fish isnt suddenly going from hard to soft water (or vice versa).
Link to video showing an acclimating method that might help you.
Fingers crossed this helps. You might want to ask the fish store if they have hard or soft water, and find out if your own is similar.
Let us know how you get on.