As far as I understand your question, the answer is "no".  Consider the Whitehead link.  

https://en.wikipedia.org/wiki/Whitehead_link

The two components of the Whitehead link are unknots (thus they are isotopic) but they do not cobound a cylinder.

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Thank you for clarifying that you wish to assume that the given link is "split": the components are separated by a two-sphere.  In this case, the link is a "split unlink": a distant union of unknots.  As Bruno points out, this is an exercise.