I have already downloaded and paid for two states. Installing Turbotax (Premier) on the new computer only installs the Federal forms. If I just transfer the .tax2019 file, will the right thing happen or do I have to do something special to get the two states installed?
Yes you need to download and install the state programs first.
After you get the program installed the first thing to do before you open your tax return is to update the program and install any state programs you had. Then open your file. So you first might need to start a fake return to be able to download the state program (go to FILE - NEW TAX RETURN)
Then go to FILE -Open and find your return.
How to download your purchase
You paid for 2 states? After the first free state? So you have 3 states? Access your paid state downloads here
https://shop.turbotax.intuit.com/commerce/account/secure/login.jsp?pagecontext=download