can't migrate due to newer OS X version

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As you noticed, you cannot restore a backup made with a newer OS X version than the one your Mac is using. If you managed to do it, you would have damaged OS X and you would not be able to boot your Mac anymore without reinstalling OS X.

Knowing that, the best solution (apart from upgrading to El Capitan again and restoring the backup then) is to restore your files from your Time Machine backup manually. This means that you would have to plug your Time Machine drive, access to it through Finder and navigate through the folders until you get to your user folder. Then, copy all your files manually to your Mac. This is a very slow process but your Mac will still be working.

Apart from that, I do not recommend you to restore any application by using that method. Some apps require additional files stored in system folders and they may not work even after putting them back into Applications folder. In this case, just reinstall them again.

I don't think you can use Migration Assistant in the way you are trying to. You need to copy (don't use Time Machine for this) your data files onto a backup disk. Once you have Yosemite installed you copy them back into your user account.

Yosemite versions of some applications may not open data created by El Capitan versions. This is not, however, a common issue IME.

C.

The process you suggest to do erases everything on your Mac and restores the whole backup. This means that you would be back to OS X El Capitan, and it looks like this is not what you want.

You're welcome!

Just ran into the same issue. I have an older Mac that can only have El Capitan as it's OS. I erased it to get all my data off and set up a clean install for my son to use. I was going to manually move back his data from a TM backup but his account/folder is not showing up in the main User folder of the backup. Any thoughts?? Thanks for any help...