I think I get what you’re saying, but let me clarify.
Multi-colour Codexes have two penalties.
The first is that the first Tech building or Add-on that they build costs 1 extra gold, and only the first time.
(For instance, if for some reason you built a Tower as your first building, it would cost 4, and then if it was destroyed and you built it again immediately, it would only cost 3.)
This one only applies if you have to different colours in your codex (neutral doesn’t count as a colour, so it doesn’t count towards this penalty).
The second penalty specifically relates to starting deck spells, and not hero specific spells, since they can only be cast by their specific hero anyway.
So yes, the second penalty is any hero casting a basic spell that is of a different colour to them (other than neutral) costs 1 extra gold.
This does mean that a neutral hero casting a coloured spell still pays 1 more.
Basically, Sirlin wanted all mono-colour Codexes to be viable always, so he specifically put these in place to prevent multi-colours from becoming totally dominant. It has definitely been shown that there are a lot of very, very strong multi-colour codexes, even with these penalties, and they would be vastly stronger without them, since early game gold is the most important gold.