I don't think Trinity knew Neo would see the tattoo, but she knew there was a good chance he'd see it. On his computer, Trinity typed:
Follow the white rabbit.
Knock, knock, Neo.
Neo hears the knock on his door immediately after Trinity told him about the white rabbit and the knock. Trinity connected the white rabbit with the door knock in Neo's mind and made it more likely he'd notice it.
Dujour's clothing is revealing enough that the tattoo is always visible, even when she's just standing next to Choi. We can still see it (barely) in a different shot during the scene (taken from this Youtube video):
The tattoo would be even more obvious without the shadow and if the camera was focused on Dujour instead of Neo. Trinity knew the tattoo was highly visible because she and other Matrix hackers can see into the Matrix from the real world. Her view of the Matrix would be in green code, but that same view is good enough for Cypher to identify "blondes, brunettes, and redheads" in the Matrix from it.
Even if Dujour didn't hug Choi and expose her tattoo to Neo (and Neo declined to go with them), there's still a good chance Neo would see it when Dujour turned around to walk away from Neo's door and go to the club. Neo would just have to keep his door open long enough to watch Dujour turn away.
Trinity wanted Neo to follow Dujour since she would lead him to a noisy club, which would be an ideal meeting place to talk about the Matrix. But even if that failed (because Neo didn't see the tattoo and didn't go to the club), Trinity still had control of Neo's computer and could try to get him out of his apartment some other way. She could, for example, tell him via his computer
Didn't you see the white rabbit on the girl? Follow her.
Obviously this is less satisfying plot-wise, but it works perfectly well in-universe. Alternatively, Trinity could have explicitly set up a meeting with Neo via his computer, ordered pizza delivery for him and told him to follow the pizza guy, etc. The Agents didn't pick up Neo until the next day while he was at work, so Trinity had all night to get Neo out of his apartment and coax him into meeting her.