While it is ultimately DM discretion, I tend to swing the other way in my opinion in that it feels like tying someone up should be a much more involved action than, say, chugging a potion.  Though they have cut down a lot on rules bloat for 5e, I do still remember from 3.5 when it felt like they tried to meticulously stat out everything from swinging swords to farting.  In that, at least, it took a full minute (or ten full rounds) to properly tie someone up.  If it were me, that still seems like a reasonable timeline (unless you were just slipping a quick loop around their wrists- but then I would let them pull a weapon and fight if they so chose, albeit with disadvantage).