Lots of fleas are quite happy living on lots of animals, for example most fleas found on cats are actually the dog flea - the fleas don't seem too worried. Saying that, these fleas can bite but not live on humans so there are differences cross species.
I would definitely not let the cat in any more as you already suggested. Some people just never flea treat their cats
A good way to look for fleas is if you have one of those clear cylinder type vacuums such as a Dyson, you can hoover the room then look for fleas pinging around inside the cylinder bit.
Look for flea faeces on your hamster, tiny red / black specs in the fur. If you rub this on damp kitchen roll & it leaves a brown / red trail then it is likely flea faeces - the colour is due to the fleas's digested blood meals. If you find this, I would talk to your exotics vet & find out which treatments are suitable for hamsters.
You can get flea treatments for your house if needed BUT I would be very careful in using this without proper exotic vet advice as your hamster free-ranges on the floor & you wouldn't want to cause problems from unsuitable insecticide getting into your hamster's system.
The flea lifecycle takes a few weeks (google flea lifecycle for loads of useful diagrams) so I would check regularly for a good few weeks in case of new ones hatching.
Hopefully you have caught it before it has gone too far & you won't find any signs of fleas