I think you will know and trust your intuition. I never had the experience of a natural miscarriage (though that was what I would have preferred, just after 3 weeks off work sitting around doing nothing (I have a 3 hour commute so I couldn't chance it), I couldn't take any more time off to wait around). But certainly the heavy bleeding I did have was shocking enough and I think you couldn't mistake what was happening for something else.
I think the main thing they will be worried about is if it isn't complete and there is anything left inside, which can lead to an infection. Again, you will most likely know (pain and bleeding that lasts longer than it should). Bleeding can last a week or so normally, but it shouldn't be accompanied by much pain and it shouldn't be really heavy. If all is fine after, you probably don't need to follow up unless you feel you need to. If you feel unwell, it would be good to get checked out. My friend had a mc just before me and it wasn't complete, so she ended up with an infection and needing to go in for surgery anyway. She was much further along though (12 weeks). Usually when they are earlier on, they are much more likely to be straightforward, so hopefully it is for you.
I don't know where you live, but if you are in the UK, I would call your Early Pregnancy Unit for a follow up. The GPs often don't know much and will likely just refer you to the EPU. Even though I wasn't even booked in with the midwives yet at 8 weeks when I found out, they were lovely and saw me straightway and were very supportive throughout. You might not need to see them at all, but if you have any questions, they are happy to talk with you over the phone.