Please clarify - are you referring to tasks in the project view or only on the "today" list? The order should be maintained within the project, but the today list will always sort your tasks automatically according to their due time and priority. If you wish to maintain a certain order of tasks on the today list, please assign due times to them, for example: tomorrow at 8:00, tomorrow at 8:05 etc.
Please make sure that you have the correct time zone set up in your Todoist Settings, your computer and your phone.
Also, try to add a couple of tasks with different specific times, for example "today at 18:30" and see if the time of the task also changes on your phone.