There are no steps (and time) in linear buckling just loads. I hope also your loads step 1 and step are different otherwise this does not have any meaning just apply 1 psi and you will get the eigenvalue load multiplier.
So like in the example you have load 1 and load 2 acting on the structure of course at the same time (since as we said there is no notion of steps and time in linear buckling). Hence why we only want to scale one external load only and not self weight.
If the time and the order they act is important you need a nonlinear analysis.
So in the sample we had A=1 for the applied load (which is your load 2) which we want to scale, and self-weight which is your load 1 which we do not want to scale. They got an eigenvalue of 100 and that scaled the load 2. So we have A=100 in the next step, and then we get an eigenvalue of 1.1 which made A=111. The total load is F=111(A) + 1.1*Selfweight.
Hope this is more clear now.
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