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Nature of Business and Summary of Significant Accounting Policies - Revenues Related (Details) - USD ($)
 12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Accounts receivable, net $ 297,427,000 $ 266,742,000    
Deferred income taxes 6,006,000 13,805,000    
Other assets 79,163,000 36,254,000    
Other accrued liabilities 32,454,000 31,025,000    
Deferred revenue 111,016,000 103,335,000    
Stockholders' Equity Attributable to Parent 289,767,000 287,437,000 $ 466,183,000 $ 481,316,000
Capitalized Contract Cost, Net $ 33,700,000 27,100,000    
Capitalized Contract Cost, Amortization Period 10 years      
Capitalized Contract Cost, Amortization $ 5,000,000.0 4,500,000 $ 4,200,000  
Capitalized Contract Cost, Impairment Loss $ 0      
As Previously Reported        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Accounts receivable, net   208,865,000    
Deferred income taxes   20,117,000    
Other assets   12,431,000    
Other accrued liabilities   30,457,000    
Deferred revenue   52,215,000    
Stockholders' Equity Attributable to Parent   263,737,000    
Accounting Standards Update 2014-09 | Adjustment        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Accounts receivable, net   57,877,000    
Deferred income taxes   (6,312,000)    
Other assets   23,823,000    
Other accrued liabilities   568,000    
Deferred revenue   51,120,000    
Stockholders' Equity Attributable to Parent   $ 23,700,000