As X said, it DOES sort of tip the opponent off that you have something to hide, but whether they can identify 'you'... especially using something like Tails that spoofs your mac address and leaves no trace that you've ever done anything more than power up at a given time.
So if you're in some internet cafe in Singapore with a hundred other people walking in and out using the connection, the IP of entrance to the tor network just doesn't do a lot to identify you unless perhaps you're already being surveilled.
Over time, if under surveillance the opponent could find a correlation between your presence and tor's use. Again, that why I've said 'the more users the better'. If everyone in that Singapore cafe was using it. the opponent would still be drawing a blank about your identity.
Yeah, in this respect the difficulties of Tor are much like the difficulties of deniable encryption. Using it at all is in a certain way incriminating. Its one of the main reasons why I try to explore novel, legitimate uses of Tor, quite apart from anonymity. It's ability to reach beyond firewalls for hosting is quite novel; unfortunately there isn't much legitimate purpose for this. Personally I don't have a problem with exfiltrating/liberating data from corporate coffers, but it is generally frowned upon more widely. But I wonder if there is a market for such an Internet cafe. An internet cafe that provides wifi for your device, and a few on-premises computers, and tunnels all connections through Tor as a matter of policy. I'd certainly hang out there, just as a matter of geek-chic if nothing else. Could also serve as a kind of base-of-operations for wider public education about cryptography, privacy, security, and so on.