I continue study SDE with Julia and I straggle with `integrator`

I’d like to get simulations like this

And I get something like that with this code:

```
rate(u,p,t) = 2
affect!(integrator) = (integrator.u[1] = 1)
jump = VariableRateJump(rate,affect!)
jump_prob = JumpProblem(prob,Direct(),jump)
monte_prob = MonteCarloProblem(jump_prob)
sol = solve(monte_prob,SRIW1(),num_monte=3,parallel_type=:threads,dt=0.001,
adaptive=false)
```

But when I change `(integrator.u[1] = 1)`

to `(integrator.u[1] = integrator.u[1]/2)`

the 1st jump occurs in the same time for all trajectories.

What does an integrator mean for the jump process?