There are two problem-sides to this argument.
The people who react. Nobody likes a movie to be spoiled but once it's done, it's done. The only thing you can do is mark the person in your mind as a [unpleasant person] and move on - while avoiding them for the foreseeable future. Throwing a fit about it is a problem.
The people who are trying to get a reaction. How they go about it is irrelevant, not being respectful of others' wishes can be a problem when it doesn't interfere with their work, and especially if it's something they shouldn't be spending their time on anyway. Depending on the workplace culture, posting sticky notes in certain places could be a problem as well.
Some members of staff (not in my department) have taken to spoiling the plot of the latest Star Wars film, upsetting other members of the company... How can you deal with this behaviour?
Largely, it depends on how your company would normally handle complaints with certain individuals and whether you, yourself are being complained to, (or have a complaint). Because, if not, I would recommend you to get over it and move on - or to tell your own staff the same so long as it isn't already disrupting normal business activity.
But, if it is disrupting normal workplace activity (and you're not the only one whose team it is affecting) If you know who it is, and know their Manager, it could be best to relay the complaints to their Manager and work out some way where both of you can continue without needing to address this ever again.
If you're legitimately worried about reputation in reporting any issue to somebody such as your manager or another manager, you can always go to HR with it. I would highly advise against sounding like you are "tattling". Just let them know what's going on and how it is affecting your, or your team's, normal work. But keep in mind that if the issue shouldn't be affecting your work, it would still reflect poorly on you.