A dusty plasma cloud hosting a counter-rotating vortex lobe pair is driven through controlled neutral-gas pressure ramps spanning nearly an order of magnitude in rate. The transient response is characterized by the longitudinal transport exponents ${\alpha }_{\mathrm{L}}$ and ${\alpha }_{\mathrm{R}}$, extracted from mean-squared displacements evaluated in the cotranslating frame of each lobe, with cluster-bootstrap confidence intervals. At baseline the two lobes are dynamically inequivalent, with a statistically confirmed asymmetry $\mathrm{\Delta }\alpha ={\alpha }_{\mathrm{R}}-{\alpha }_{\mathrm{L}}<0$ in all four experiments. The pressure ramp drives the exponents toward equalization and ultimately inverts the asymmetry. The inversion is completed within the ramp only for the gentlest forcing, and is deferred to the end of the forcing interval, or beyond it, as the ramp rate increases. A force-scale analysis shows that the per-particle neutral drag remains below the static levitation-force scale, but increases systematically with ramp rate and produces millimeter-scale horizontal advection of the cloud. The behavior is organized by a Deborah number $\mathrm{De}=T_{\mathrm{rot}}/{\tau }_{\mathrm{ramp}}$: the normalized inversion time increases with $\text{De}$ across the four experiments and approaches the end of the ramp for the fastest protocols. These results identify the vortex lobe pair as a rate-dependent, kinetically gated structure and connect its dynamics to the broader phenomenology of driven viscoelastic soft matter.

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• Transport phenomena
• Vortex dynamics
• Nonequilibrium systems