From Allen and Greenough's New Latin Grammar for Schools and Colleges
In particular, cum with the Subjunctive was used in narrative (hence the past tenses, Imperfect and Pluperfect) as a descriptive clause of time. As, however, the present participle in Latin is restricted in its use and the perfect active participle is almost wholly lacking, the historical or narrative cum-clause came into extensive use to supply the deficiency.
I'm no expert by any means, so take this with a handful of salt, but I did a quick search for cum
with a participle and didn't find anything. This above statement seems to indicate that cum is used in a participial manner, so adding a participle would be redundant.
I hope that helps.