There is an overshoot after the rise time: Why ?
The overshoot you have observed is basically the nature of the AD8309 output
stage, it takes a few moments to settle. There are one of two things to deal
with this overshoot.
1) Delay the point at which you measure the output pulse. In this case you
could just wait a few 100ns until the RSSI settles.
2) Place a small capacitance on the VLOG output to reduce the overshoot.
Something of the order of 30-50pF should be sufficient and shouldn't have much
effect on the overall response time of the AD8309.