How do transgenic transformations cause off-target phenotypes?
The C.elegans used in the study you linked was originally made by Tissenbaum &amp; Guarente using the gamma irradiation protocol.

In short, the protocol provides the injection of the desired DNA construct in the worm's gonad followed by gamma irradiation of the worms.

Upon radiation exposition, the genomic DNA of the worm will break at random sites and will undergo repairing by the appropriate cellular enzymes, during the latter stage the exogenous DNA can be integrated (ligated) into the genome. However, the genomic DNA can also acquire random mutations due to the radiation. This is how transgene insertions can cause off-target mutations in this case.

With other organisms or cells, the protocols are different. To engineer mammalian cells, for example, radiations are never used but still, you have to generate breaks in the genome to edit it. Depending on the method the "off-target rate" of a given experiment may vary, but it is never zero (not yet).