If you're falling because of ball bearings, do you automatically land on caltrops in the same space?

Question

If a creature had to make both saving throws for ball bearings and caltrops, and failed the ball bearings - Would they automatically fall prone & land on the caltrops, taking caltrop damage with no chance for a caltrops saving throw (or regardless of a passed caltrops saving throw)?

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Inspired by this answer to this question If an area is covered in both Ball Bearings and Caltrops, does the creature need to move at half speed or quarter speed to avoid both their effects? where it's mentioned:

Note that if the creature chose to move greater than half their speed across the combined area then they would be forced to make both saving throws, one against the ball bearings and one against the caltrops, possibly suffering one effect or the other effect or both effects combined.

Answer 1

No

There is nothing in the rules to suggest you do.

A DM is free to impose disadvantage on either (or both) saving throws if circumstances warrant - perhaps they do?

Answer 2

The rules don't say. Make a ruling.

The descriptions for ball bearings and for caltrops don't mention each other, so a strict reading of the rules doesn't answer the question. Apply the level of physical reasoning your group finds acceptable.