Getting the Natasha is not really that great. I managed to do it a couple of times, and they never would stay there, because someone always found out. My poor girls would get beat up by nearly every guy that they were romantically linked to.
I'm not quite sure how your sim would get the label as a cheater unless you have Generations installed. Maybe EA added that through a patch. Now as far as your sim having any problems in future relationships when she is an adult, having the cheater reputation will not cause problems in future relationships, just as long as she is only involved romantically with ONE person. I have had sims who had the cheater reputation married till they had died with no problems from their spouse. Check her relationships and make sure she only has one person she is involved with. If she is involved with more than one, then have her either break up or ask to be friends with everyone else, but one person.
To answer your question, having a lover tell (ask) her to break up with her boyfriend, yes that will cause her to be a cheater. I have only had that happen once where the sim did not get labeled as such, and it was because that sim did not get involved with the person who asked her to break up with another. That sim was in a bad relationship and she stayed single for awhile.