IIRC the whole thing about the land mines exploding when you step off of them is purely down to the Bouncing Betty or the German S-Mine, which saw widespread use and gained its infamy in WW2. They almost worked in the manner described, actually going off with a time delay rather than waiting until the hapless soldier removed his foot from the plunger. But they used a small lift charge to pop the main explosive up into the air a couple of feet and then went off, with the aim of shrapneling in a circle a whole group of soldiers passing by and not just whoever stepped on it. Obviously this wouldn't work so well if someone were standing on it at the time.

The popular conception formed that they went off "after you stepped off of them," which was true in most cases (who was going to just stand there like a nincompoop after you'd just triggered it?) and then Hollywood writers of the era just assumed that most or all landmines worked that way and wouldn't let that misconception go. So now here we are.