Usually these people will give it away through an accumulation of subtler behaviors, or they just kinda out-right say so.

These things are often subtle. Noticing the many ways they never really talk about/to you in any other way than that one aspect of you they fetishize. In this post there is the dating history, how she is just there, quietly, on his arm, because he isn't actually doing anything to interact with her outside of her being there to be his asian woman. You may say that it is her responsibility to socialize, and that can be true, but more often than not this is a learned behavior. They have come to understand he doesn't really want them being anything but his arm candy, and has a history of making things bad if she does otherwise.

A lot of this easily deniable, which is why so many people fall into it. A lot of abuse, and objectification, isn't going "hey, you are my asian fuck doll, don't try to have autonomy". Much like how racism can be expressed in a bunch of much more subtle ways, like women taking direct hold of their purse when a black man walks on the elevator, but the strange white men didn't illicit the same response. It could just be a shift of position, or a million other things that aren't racism. However, when you are a black man, and see it happen every time this situation comes up, you realize it is a response to you, and what makes you different from those she was around to that point is? You are black. Hell, people might not even be aware they are doing it.

There are some people that make it clear though, for reference see the incel community obsession with asian women.