The string is not one hash, but actually two base64-encoded values. If you take a closer look at the code you'll see that the output is generated as
System.out.println(Base64.encodeBase64String(btPass) + " " +
Base64.encodeBase64String(btPass) creates a base64-encoded string from the password hash, and
Base64.encodeBase64String(salt) creates a base64-encoded string from the salt.
base64-encoded password hash base64-encoded salt
By design and definition a salt doesn't need to be secret (it just exists to thwart attacks on a password hash via rainbow tables), so the salt can be transmitted in clear text. The base64-encoding is just to make handling easier (text is usually easier to handle than binary values).
The server only has to decode the second string to get the salt. Then it can calculate a hash from the salt and the password entered by the user at login and compare the result to the decoded first string to see if the two hashes match (i.e. if the user entered the correct password).
Addendum: To avoid confusion, you calculate and upload the hash and salt to the server only once. These are not the values you provide when you log into Solr, they're the values to which Solr compares the password you entered at login.