SQL Full Text Search - Result Order changing
Try This:

DECLARE @SearchString VARCHAR(200)
SET @SearchString = 'Adam OR West OR 60608'

SELECT Id, First_Name, Last_Name, Address,City,State,Zip, CT.Rank
FROM Patient_Ex PAT 
    INNER JOIN CONTAINSTABLE(Patient_Ex,*, @SearchString) CT 
        ON PAT.Id = CT.[Key]
ORDER BY CT.RANK DESC


Explanation:
The table produced by CONTAINSTABLE includes a column named RANK. The RANK column is a value (from 0 through 1000) for each row indicating how well a row matched the selection criteria.

Update:

Try adding weights to your keyword and see if it changes things:

DECLARE @SearchString VARCHAR(200)
SET @SearchString ='ISABOUT (Adam WEIGHT (.8), West WEIGHT (.4), 60608 WEIGHT (.2) )'
SELECT Id, First_Name, Last_Name, Address,City,State,Zip, CT .RANK  
FROM Patient_Ex PAT 
INNER JOIN CONTAINSTABLE(Patient_Ex,*,@SearchString,LANGUAGE N'English' ) AS CT  
ON PAT.Id = CT .[KEY]  
ORDER BY CT.RANK DESC;  
GO  


If the above doesn't works either try rebuilding your Catalog if you have  very few rows in database as people have reported wrong rank outputs with databases having less no of rows while the ranking working fine with database having large no. of rows,another workaround is to create dummy table in your database and index it in your catalog.
Please read this if you want to learn more about how ranks are calculated.
Source : 1,2