Windows Vista Home Premium support?

Acronis have done no testing with any Acronis True Image version since ATIH 2011 for Windows Vista so the answer to your question is that you would have to test it yourself to see if it would work or not.  I would suggest trying a trial copy of ATIH 2017 before committing to buying an extra license.

The bootable Rescue Media is effectively Windows OS version agnostic in that it doesn't care which flavour of Windows you have as it will be operating at a much lower level looking at partitions and sectors in the most part, or else looking at the NTFS file system for files and folders.

I may decide to give this a test myself if I can find the time, my laptop currently has a dual-boot Windows Vista 32-bit and Windows 10 environments where I am running ATIH 2017 on the Windows 10 OS (and backing up Vista from that side too).

Thanks Steve, let me know what you find if you time to install on your Vista partition.  Note that I HAVE connected remotely to Granny's system and successfully run True Image 2013 by Acronis and backed up to her Seagate Backup Plus Slim.

If you already have ATIH 2013 installed on the Vista system then I would stay with that, it will have much less resource impact than 2017 because it doesn't have as many bells & whistles to work with.  It sounds like you are doing the remote support too so keeping with a working solution fits with the KISS principle (Keep it Simple S!).

I do the same thing for friends and family using TeamViewer and simple is good!

Agree completely. ;)  Funny, sounds like you're the designated one within your group of family/friends like I am. ;)  Am going to reload my current XPS 8500 with Windows 7 (maybe 10) for my mom before Vista "extended support" ends next April.  Perhaps this is when I'll switch her to TI 2017.  For remote connectivity, I use Splashtop Personal from my iPad Pro 9.7 and RDP (and Splashtop) from my desktop PC.  Both work well and often result in care packages (cookies!) and/or gift cards from Techno-Granny. ;D

Eeeks!  Just found on wikipedia ... under Versions adjacent to v2016

Added support for Windows 10. Removed support for Windows Vista.

https://en.wikipedia.org/wiki/Acronis_True_Image