The answer should be set `PerformanceGoal -> "Quality"`. Otherwise `PerformanceGoal` options is set to global `$PerformanceGoal` which switches to `"Speed"` if the evaluation is done on a preemptive link. (default for most of gui/Dynamic etc).

See more in linked duplicate.

However, [there appears to be a bug in 11+][1] which makes this option being ignored, fortunately Mathematica is great in workingaround bugs it introduces. So instead using the option we can `Block` the `$PerformanceGoal`:

    Animate[
        Block[{$PerformanceGoal = "Quality"}
          ,  Plot3D[Sin[t x y], {x, -3, 3}, {y, -3, 3}, PlotRange -> {0, 1.2}]
        ]
      , {t, 0, 2}
      , AnimationRunning -> False
      , DisplayAllSteps -> True

    ]
[![enter image description here][2]][2]


  [1]: https://mathematica.stackexchange.com/q/146214/5478
  [2]: https://i.sstatic.net/D2nuV.png