Take an experience I had recently with a perhaps Ni friend. We were getting fast food and pulled up to the first window to pay. I paid, and the guy who took my money said "Wait right here, I will be right back with your food". So I'm waiting, and after two long minutes the Ni in my backseat starts getting irate, telling me to pull up to the second window, the guy is probably waiting for us to pull up. I tell him several times the guy explicitly instructed me to wait there, and my friend in the passenger seat confirms this, but the Ni is having none of it. He starts mumbling curses to himself, boiling about how wrong I am, repetitively expressing how 'fucking stupid' the situation is. My face grows hot in contemplation; in my mind I start doubting my perception - "did he actually instruct me to pull forward? Should I pull up regardless? He is right, this is quite odd..." Then I think to myself "Okay, if the guy was actually waiting for me he would have A) opened the window and waved me forward or B) walked my food back to the first window anyways. There is a car behind me, he obviously isn't just going to let me hold up the line this way. Plus, it's three in the morning - they are probably taking so long because they are making this food fresh since they are not all that busy." So I decide to ignore Ni (including my own) and wait.
Sure enough, about a minute later, the guy opens the window and hands me the food cheerfully. I felt like turning around and smacking the guy in my backseat for causing me so much cognitive dissonance, but I realize this is just Ni being Ni. He had no intent to reconcile the fact that the man explicitly instructed me to wait to the patterns he had recognized in the past. This is a textbook example of Ni suppressing objective sensory experience in the manner Jung describes. So Se is in the moment, to this regard, in the sense that it correctly objectively understands and interprets such experience.
I have postulated while recanting this story if it could be attributable to Si - but no, it couldn't. Jung states Si to be over reliant on Se, Se is Si's unconscious attitude - perhaps too trusting of sensory experience, much as the way Ni is too trusting of its intuitive experience. Now - it may be I am going quite out on a limb with this story being attributable to Ni altogether, but I feel confident in my thoughts and I would welcome a rebuttal should anyone disagree.