I believe this may have happened to me once, when using paste (leaded 60/40) I believe some of it got spilled on to the top of a DIP chip that was sitting nearby to where I was working. The chip was one which got plugged in to a socket, so never went through an oven which was used for the SMD parts on that went on the board before inserting the chip. After putting the board through the oven, it and the chip went in a semi-enclosed anti-static bag and I think I put that in to my rucksack to take across to a different building. All manner of other things, including a packed lunch would have been in other compartments of that rucksack. It was only some days later when I plugged that DIP chip in to a socket that I noticed a large grey powdery "stain" upon it. It had been several days between my most recent use of paste and the day I found the stained chip, in the intervening time some traces of the paste might well have gotten in to all manner of places.
My suspicion, though by no means a certainty, is that only quantities of powdery material which are sufficiently large and dense to be seen are likely to matter. The lead-tin balls within solder paste are not infinitesimally small anyway, so there's going to be a minimum size below which the only thing you could have is the same tiny trace quantities of lead atoms rubbed off on to other surfaces that you might get with solid wire solder. For ordinary wire solder I'd tend to suspect worrying about secondary contamination (your hand touches the solder, then your hand touches a laptop mouse or such, do you at that point consider the mouse contaminated) is an entry route to paranoia, whereas cleaning your hands and surfaces that the solder has directly touched makes sense. For paste, it can definitely spread more, but if you can't see any signs on a surface and can't see any signs after a very cursory glance under magnification, then there probably isn't any further contamination.
I didn't wear gloves for solder pasting, but I was doing it with a needle and pump setup, so there'd be less of it spreading around than with stencils. Definitely a separate area for it away from anything else. For a start, I can't think the little balls of conductive material would be all too good for a laptop if some got in to the USB port or other exposed parts.
For hard surfaced items a few successive rubbings with wet and then dry, tissue paper should help. Wet with IPA rather than water in the case of sensitive electronics like a laptop, and even then only a pretty small quantity, sprayed on to the tissue not on to the laptop. I've also found placing duck tape on a surface then peeling it off can remove residues that tissue rubbing might not.