As SIB said, the Neem will help to make sure that the mites do not come back. But, that being said, there are no guarantees. You will want to continue to use the Neem. The DE, in my experiences will only work while it is dry, so as soon as you water it the first time, it's effectiveness dwindles. You may need to use something stronger if the Neem does not work 100%.
That being said, all of my pots have been re-used and we have a pretty significant aphid presence in our area. It is all about keeping up with the deterrents. As long as you treat the plants regularly they will be fine. Just make sure that you stop using whatever it is a few weeks before you harvest anything, and wash any leaves before ingestion
Hope this helps. Have a blessed day.
May we continue to be blessed