I think that you are not referring to the right reason why your former students cannot simply go on and publish the small projects they did under your supervision in lower-tier journals (or any other journal for what matters).

It's not that the work done in the lab belongs to the PI and the lab as a group, it's that you and possibly other people in your group contributed to these projects, at least by providing scientific guidance and supervision.

As such, they cannot claim that the work is solely theirs by not mentioning you as co-authors and, as a corollary, cannot publish without your explicit consent.

I think that you are not referring to the right reason why your former students cannot simply go on and publish the small projects they did under your supervision in lower-tier journals (or any other journal for what matters).

It's not that the work done in the lab belongs to the PI and the lab as a group, it's that you and possibly other people in your group contributed to these projects, at least by providing scientific guidance and supervision (I think the answer to your question is to explain them that bit).

As such, your former students cannot claim that the work is solely theirs by not mentioning you as co-authors and, as a corollary, cannot publish without your explicit consent.

I think that you are not referring to the right reason why your former students cannot simply go on and publish the small projects they did under your supervision in lower-tier (let me guess, author-pay) journals.

It's not that the work done in the lab belongs to the PI and the lab as a group, it's that you and possibly other people in your group contributed to these projects, at least by providing scientific guidance and supervision.

As such, they cannot claim that the work is solely theirs by not mentioning you as co-authors and, as a corollary, cannot publish without your explicit consent.

I think that you are not referring to the right reason why your former students cannot simply go on and publish the small projects they did under your supervision in lower-tier journals (or any other journal for what matters).

It's not that the work done in the lab belongs to the PI and the lab as a group, it's that you and possibly other people in your group contributed to these projects, at least by providing scientific guidance and supervision.

As such, they cannot claim that the work is solely theirs by not mentioning you as co-authors and, as a corollary, cannot publish without your explicit consent.