We've found that installing directly under No Parent has its own problems, so:
It seems that installing a brand new style under an existing parent is also causing issues.
Ultimately, talking to your style author is probably the best bet.
Otherwise, what problems are you seeing when you install the new style to the top level?
Generally speaking, and my understanding is, your Styles area in AdminCP should be looking something like:
Default (No edits here)
-- Child of Default (edits allowed)
Style 1 (No edits here)
-- Child of Style 1 (edits allowed)
New Style (No edits here)
-- Child of New Style (edits allowed - Master edits - maybe things like alignments or footers etc)
--- Child of Child of New Style (edits allowed - tweaked edits - maybe Dark version)
--- Child of Child of New Style (edits allowed - tweaked edits - maybe Light version)
and so on for each style.
When you add a completely new style, you need to start from scratch and add it like New Style above. Then create children that you can edit. The parent attributes propagate down through the children unless overridden in the children. When the style author releases an update, you update the top level parent which should leave the children and your edits untouched.
It's been a long time since I've bothered playing in mine, so maybe I'm not remembering properly. Happy to be corrected (or confirmed) if need be.