Will the ECs from a minor at another LDE university automatically be mentioned on my transcript?

No, this does not happen automatically. You are responsible for registering a list of marks for the minor with your own student administration. For this, you must have a list of marks showing the obtained results. Based on this list of marks, you can get your results registered at your home institution. The list of marks for the minor can be obtained as follows:

Leiden University:
Contact the education administration office of the programme in question.

TU Delft:
At the end of the minor you will receive a list of marks with all the study results by post.

Erasmus University Rotterdam:
Go to the examination administration of the relevant faculty with a valid proof of identity. This is located in the E Building in Rooms EB-29 to EB-42. Opening hours: Mon-Fri 9.00 to 16.00.