In NONMEM, you write a regression type expression like Y = F(1 + EPS(1)) + EPS(2) which in math would be
Y = f(\theta,\eta)(1 + \varepsilon_1) + \varepsilon_2
where \varepsilon_1 and \varepsilon_2 are Gaussians with variances \sigma_1^2 and \sigma_2^2 and typically uncorrelated. Hence you have that
\mathrm{E}(Y|\eta) = f(\theta,\eta) \\
\mathrm{Var}(Y|\eta) = f(\theta,\eta)^2 \sigma_1^2 + \sigma_2^2
In Pumas, you specify the conditional (on the random effect) distribution of the dependent variable and the Normal in Julia is parameterized by its standard deviation so you need to take the square root and you end up with
Normal(cp, sqrt((cp*σ₁)^2 + σ₂^2))
if you parameterize with two standard deviation parameters. I hope it answered your question.