It might help to see the schematic.
Not having a schematic to work from, it looks like this might be "normal" operation. As a matter of explanation, consider that the current limiter is a feedback loop. To have a stable loop, the current limit amplifier gain (it is a gm output amplifier) is relativey low for "small" inputs, but has a non-linear acceleration for large inputs. On a test unit, this corner occurred at about 80 - 100mV. The fast turnoff speed is indicated in the datasheet "Large overload response time" and this is the condition the enabled "GATE sinking current" strength is specified.
A gm amplifier has an expression of I(out) = A x (delta Vin). This means that for a very small overload the gate drive is small, getting larger as the deltaVin gets larger. This accounts for the apparent acceleration seen in the gate voltage (integral of the gate current). The other part of the apparent delay to control is caused by loop saturation - the gate must be discharged to around the threshold where actual control can take place. This saturation/delay also occurs on the other side of a fast protection (or a case where the amplifier gain is too high) in that GATE can slew so fast that the MOSFET is off before the amplifier can recover and attain regulation.
The result of the TPS2490 implementation can be seen in the waveform. For relatively small overloads, abrupt limiting with voltage transients and potential load dropouts is avoided (when limiting occurs, the output capacitor discharges and for a converter load, the current goes up). The system just rides through. If the small overload is prolonged, it is contained in a soft, smooth, stable limiting. You can see that the loop responded and a smooth stable current limit was reached. If a hard load short occurs, the TPS240 responds quickly to attenuate it (not seen in the figure).