Connecting a 30 amps generator to a 20 amps transfer switch

I bought my house from an electrician who had redone the entire wiring. In particular he'd put a transfer switch for a generator. It's
an EmerGen switch from Connecticut Electric and it looks like it's rated 20A (There's a L14 male plug with a big "20" above it. I bought an L14-20 female connector and it seems to fit)
I didn't think I'd ever need it but sure enough last winter our region experienced its worst wind storm in almost 15 years. We were without power for 7 days! I was able to secure a generator on the 3rd day but everybody was out of the L14-xx cords so we had to use regular extension cords and creative wiring (we hotwired the furnace's blower and such... nothing horribly dangerous but I'd rather not repeat that if I can).
Anyway, this year I vowed to get ready. I checked the generator and realized that it is rated 30 amps. The front panel has an L14-30 female plug. So I want to hook up my generator, which is rated 30A to my transfer switch, which is rated 20A. I have an L1420 female connector for the panel, an L1430 male connector for the generator, and enough wire (rated 30 amps) to go in between. I can theoretically build my own cable and hook the generator to the panel
My question is: is it safe?
I believe it should be. However I am also enclined to doubt myself (the memory of those EE classes in college and the dismal grades that ensued helps).
I believe that, should my appliances draw more than 20A, the breakers on the panel will trip. The generator _can_ deliver *up to* 30A but that doesn't mean it will. It only does if the appliances on the other end actually require that much current. As long as I don't overload my circuits everything should be fine. I the appliances were to draw more than 20A then the circuit breakers on the transfer panel would trip.
Does anybody see any issue with my reasoning? Can I proceed with my plan or should I replace the transfer switch with one that is rated 30A?
Thanks for your help!
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Apparently this is what you have. http://www.connecticut-electric.com/media/EGSCutSheet.pdf
Install a 20A breaker between the generator and the switch.
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