You may please use ConstraintDate and ConstraintType to set the desired data. Please give a try to the following sample code and share the feedback.
Project asProject = new Project(@“Empty_Project.mpp”);
asProject.Set(Prj.StartDate, new DateTime(2017, 2, 6, 8, 0, 0));
asProject.CalculationMode = CalculationMode.None;
Aspose.Tasks.Task f01 = asProject.RootTask.Children.Add(“Task 1”);
f01.Set(Tsk.Start, new DateTime(2017, 2, 6, 8, 0, 0));
f01.Set(Tsk.Finish, new DateTime(2017, 2, 10, 17, 0, 0));
f01.Set(Tsk.Duration, asProject.GetDuration(5, TimeUnitType.Day));
f01.Set(Tsk.ConstraintType, ConstraintType.StartNoEarlierThan);
f01.Set(Tsk.ConstraintDate, new DateTime(2017, 2, 6, 8, 0, 0));
Aspose.Tasks.Task f02 = asProject.RootTask.Children.Add(“Task 2”);
f02.Set(Tsk.Start, new DateTime(2017, 2, 13, 8, 0, 0));
f02.Set(Tsk.Finish, new DateTime(2017, 2, 17, 17, 0, 0));
f02.Set(Tsk.Duration, asProject.GetDuration(5, TimeUnitType.Day));
f02.Set(Tsk.ConstraintType, ConstraintType.StartNoEarlierThan);
f02.Set(Tsk.ConstraintDate, new DateTime(2017, 2, 13, 8, 0, 0));
Aspose.Tasks.Task f03 = asProject.RootTask.Children.Add(“Task 3”);
f03.Set(Tsk.Start, new DateTime(2017, 2, 20, 8, 0, 0));
f03.Set(Tsk.Finish, new DateTime(2017, 2, 24, 17, 0, 0));
f03.Set(Tsk.Duration, asProject.GetDuration(5, TimeUnitType.Day));
f03.Set(Tsk.ConstraintType, ConstraintType.StartNoEarlierThan);
f03.Set(Tsk.ConstraintDate, new DateTime(2017, 2, 20, 8, 0, 0));
asProject.Recalculate();
asProject.Save(“output.mpp”, SaveFileFormat.MPP);