Photos cropped from what they looked like on the viewfinder?

Hi. I'm an amateur photographer. I had a Nikon D5100 and used primarily a Nikon 35mm f1.8 prime lens on it. My D5100 broke, I figured I might as well upgrade, and I bought a full frame D610. I am now using my 35mm prime on it. I was doing a session last night and something really annoying kept happening: I would see the photo in the viewfinder, say like my subject would be totally shown head-to-toe, but then when I took the picture, half his forehead would be cut off. It's like it would be cropped.

Is this happening because the 35mm is not totally compatible with the D610? Is it a DX lens? If so, what is a lens I could buy that is made for full frame cameras so that wouldn't happen? I really wanted to buy a Rokinon 85mm 1.4, but I don't know if that's a good choice.

And Please, for the LOVE OF GOD, don't be an a**hole about this question. I said I'm an amateur. Yes, I know, as so many "real" photographers have been so rude about before, I have NO business with a full frame camera because I'm just a dumb kid that knows nothing and doesn't belong in your field. I swear photographers can be so rude when I ask questions and they need to chill--i'm not trying to take your business or something okay, actually I'm attending college to be a pilot and this is just a hobby, and I'm just trying to get better. So please, if you can't help in a nice way, feel free to stay away. Sorry for those of you who weren't going to say something rude.

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