Black hole X-ray binaries undergo occasional outbursts caused by changing inner accretion flows. Here we report high-angular resolution radio observations of the 2013 outburst of the black hole candidate X-ray binary system J1908+094, using data from the VLBA and EVN. We show that following a hard-to-soft state transition, we detect moving jet knots that appear asymmetric in morphology and brightness, and expand to become laterally resolved as they move away from the core, along an axis aligned approximately $-11$degree east of north. We initially see only the southern component, whose evolution gives rise to a 15-mJy radio flare and generates the observed radio polarization. This fades and becomes resolved out after 4 days, after which a second component appears to the north, moving in the opposite direction. From the timing of the appearance of the knots relative to the X-ray state transition, a 90degree swing of the inferred magnetic field orientation, the asymmetric appearance of the knots, their complex and evolving morphology, and their low speeds, we interpret the knots as working surfaces where the jets impact the surrounding medium. This would imply a substantially denser environment surrounding XTE J1908+094 than has been inferred to exist around the microquasar sources GRS 1915+105 and GRO J1655-40.