One illustrative IC product disclosed herein includes an isolation structure that separates a fin into a first fin portion and a second fin portion, an epi semiconductor material positioned on the first fin portion in a source/drain region of a transistor device, wherein a lateral gap is present between a first sidewall of the epi semiconductor material and a second sidewall of the SDB isolation structure, and a conductive source/drain structure that is conductively coupled to the epi semiconductor material, wherein a gap portion of the conductive source/drain structure is positioned in the gap and physically contacts the first sidewall and the second sidewall.