Allstate Trop Cyc Ins - Do I pay full ded up front?

I currently have Allstate homeowner's insurance. My policy identifies a 5% tropical cyclone deductible. I asked Allstate about this and they assured me that I would only have to pay 5% of the repairs up to the maximum amount. Speciifically I asked what would happen if I had $20K worth of damage and my deductible was $15K. Do I pay my $15K first? They said no, I would only pay 5% of the $20K repair. Was I told correctly? Who has better insurance?