OK, it took me quite some time to figure this out so I thought I should share my notes here so you don;t have to get trhough that process too.
Since Sonoff mini are now shipped with firmware >3.3.0 the jumper/DIY tool flashing method does not work anymore - believe me, I lost maybe 2 hours trying to get this method to work 
This is actually way more simple - once you know the process… It requires some few extra software tools (docker and postman) but you don’t need to open the mini to put a jumper, download DIY tool or the ewlink app. I wonder why they still ship the module with the jumper since it’s useless now… All of this can be done with your computer (I use a mac but all this tools are available on Windows too.
My best source was this article that I found after about 1000 google requests. My notes below are very heavily based on that article but cover the whole process from the box opening to a fully running Tasmota device.
Hope this will help you too!
How-to flash SonOff mini > 3.3.0 with Tasmota (to this day):
- Download latest ‘LITE’ Tasmota Firmware: https://github.com/arendst/Tasmota/releases
- Calculate SHA: sha256sum Downloads/tasmota-lite.bin (or use a sha256sum website)
- Plug in the sonoff module
- 5s long press on module physical button
- Search and connect to ITEADxxx wifi network, password is 12345678
- Browse to http://10.10.7.1/
- Set same wifi as computer (not your iot wifi or next steps wont work)
- Connect your computer to that same wifi
- Retrieve sonoff IP from your router most recent connections list
- Download and import Lukas’ postman collection: https://gist.github.com/lukaskukacka/08a3c8cf20d50ccc522a71ef9ad952ee
- Set or update baseURL Postman variable with SONOFF_IP:8081 (Eye button in Postman)
- Call http://{{baseURL}}/zeroconf/ota_unlock
- Start nginx-file-browser docker container:
docker run -p 8000:80 -v ~/Downloads/:/opt/www/files/ mohamnag/nginx-file-browser - Call http://{{baseURL}}/zeroconf/ota_flash - you need to set the right downloadUrl (something like http://yourcomputerip:8000/files/tasmota-lite.bin) and sha256sum (step 2 above) values in the body request. Wait ~1 minute for completion (you can check docker logs to see if it’s still downloading the file…).
- Search and connect to new Tasmota wifi
- Setup device to your iot wifi
- Retrieve Tasmota IP from your router (should be the same)
- Setup Tasmota template:
{"NAME":"Sonoff Mini","GPIO":[17,0,0,0,9,0,0,0,21,56,0,0,255],"FLAG":0,"BASE":1} - Setup Tasmota MQTT
- [Setup Tasmota switch mode]
- [Add new device to Tasmoadmin interface]