Soldiers don't spike their drinks. At Prison Island, the leaders there saw how powerful they were and invite them to tempt them to their side. There's bunch of drugs and alcohol, yes, and women tempting men left and right but the 2 MLs don't pay attention to this and MC just leaves the room early on. Someone who's a comrade of this guy in Prison Island that follows MC offers the 2 ML some cigarettes (or cigar). Since the end of the world started, they hadn't smoked since getting cigarettes wasn't as important as gathering food. Since the guy was an ally of someone MC trusted, they trusted that the cigarette wasn't drugged. The person who MC trusts sees them smoking and warns them too late that, although it isn't drugged or dangerous, for first time smokers, it acts as an aphrodisiac (it's a handmade end-of-the-world cigarette made from plants from that time). After that, it's just as @kiara8 explained.
Later on, 2nd ML is seen smoking it again near the cliffside and makes MC smoke it too before having beach sex.