SDDE: saveat causes incorrect evaluation of the history function

[ChrisRackauckas-Claude]

Moved from SciML/StochasticDelayDiffEq.jl#52.

Using saveat with SDDE problems causes the history function to return incorrect values. When solving without saveat, the history function evaluates correctly, but adding saveat changes the results.

Reproducer (adapted for new DelayDiffEq-based SDDE):

using DelayDiffEq, StochasticDiffEqLowOrder

function f(du, u, h, p, t)
    du[1] = -u[1]
    println(h(p, t - 0.001))
end

function g(du, u, h, p, t)
    du[1] = 0.1
end

tspan = (0.0, 0.1)
h(p, t) = 0.0
u0 = [0.0]
prob = SDDEProblem(f, g, u0, h, tspan, 0.0, constant_lags = [0.001])

sol = solve(prob, MethodOfSteps(EM()), dt = 0.01)           # correct
sol = solve(prob, MethodOfSteps(EM()), dt = 0.01, saveat = 0.1)  # incorrect history

The history function should return the same values regardless of saveat.