Regarding Falmouth (since you asked about it), we've done the ziplining and waterfall climb (booked through RCI), and Hilton Rose Hall and Hyatt Zilara day-passes (booked through Resort for a Day). Regarding feeling safe, I really do think that's up to everyone's particular experience which certainly does vary.
The last two times I was there, at some point in our drive, we would come to a town where there were military with machine guns at a certain checkpoint. One side of my brain can say, "Thank goodness there are people to keep everyone safe" and then there's the other side, "Wait, are we NOT safe? Why are these guys here?" so it's all how you look at it. For me, that raised more questions of safety than it did provide comfort but I tend to deal with anxiety.
However, once at the hotel property, I felt perfectly safe. Ironically, the hotels I visited are also protected by guards at the gate -- so I have had to readjust how I view any trips to Jamaica knowing that is just the way it is there (or was, it has been some years now).