When there are both starting values and conic constraints, the optimal value is the third solution and the first solution is just the starting value.
using JuMP
using MosekTools: Mosek
solver = Mosek.Optimizer
model = Model(solver)
@variable(model, x, start=2)
@constraint(model, [x, 1] ∈ SecondOrderCone())
@objective(model, Min, 2x)
optimize!(model)
@show termination_status(model)
@show primal_status(model)
@show primal_status(model, result=2)
@show primal_status(model, result=3)
@show value(x)
@show value(x, result=2)
@show value(x, result=3)