Hi @RupaJ
You should follow the same sequence that you had followed while doing a fresh installation. If you are looking for specific order then it's as per the plan file. While installing the software binaries there isn't much dependency and the sequence wont' matter however while performing the configuration part the sequence matters and mostly it's meta first, followed by compute and mid-tier. It can be different as well, depending on what products are installed and configured at your site.
Usually it should not update the configuration for mid-tier if you have selected for meta. I am not sure on what could have happened during the update process.
For the backup, I hope you have taken a cold backup of all the tiers before the update process? If yes, that should suffice. Once the updated is completed successfully, do take another cold backup for a restore point.
Hope this helps!