Integratror interface skips timesteps in DifferentialEquations.jl?

I have a question about the integrator interface of the DifferentialEquations package. I want to step through the solution process of a set of coupled ODEs (to wich I want to add a nonlinearity that I can’t use a callback for).
My issue is the following: the documentation gives the possibility of solving the integration problem step by step via

for i in integrator

However, it only exposes every second integration step. Why is this? How can I get access to every integration step?

Here is some sample code to demonstrate this:

using DifferentialEquations
#using CairoMakie for plotting

function dynamics!(du,u,p,t)
    du[1] = 1. 

    u0 = [0.]
    t = 1.
    dt = 0.1
    tspan = (0., t)

    prob = ODEProblem(dynamics!, u0, tspan, dt = dt);
    integrator = init(prob, Euler(), save_everystep=true)

    for i in integrator #simulation loop
        @show i, integrator.iter
    usol = [x[1] for x in integrator.sol.u]

""" #for plotting
    f= Figure()
    ax = Axis(f[1,1])
    lines!(integrator.sol.t,usol, label = "u")

The output of the above code is the following:

(i, integrator.iter) = (t: 0.1; u: [0.1], 1)
(i, integrator.iter) = (t: 0.30000000000000004; u: [0.30000000000000004], 3)
(i, integrator.iter) = (t: 0.5; u: [0.5], 5)
(i, integrator.iter) = (t: 0.7; u: [0.7], 7)
(i, integrator.iter) = (t: 0.8999999999999999; u: [0.8999999999999999], 9)

As one can see, the integrator only exposes uneven integration steps. Why only uneven steps? Is there an option to expose all integration steps?

step!(integrator) is advancing the integrator by a step. Remove that line and everything will work.

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