You have to put really in this position as if you change it, the meaning will change slightly. It’s a really expensive car. = It's a very expensive car. It’s really an expensive car. = It is in fact an expensive car. You could use quite in either position with the same meaning. It’s quite an expensive car. = It's a quiet expensive car. I think the first version is just easier to say, so that's why it's more common.

"Really" and "quite" are handled in the very same way. You can say (1) "it's a really expensive car" or "it's a quite expensive car". You can also say (2) "it's really an expensive car" or "it's quite an expensive car". For the sentences in (1) the adverbs "really" and "quite" modify the adjective "expensive". For the sentences in (2), the adverbs modify the verb "is", and this causes a slight variation in the meaning.

That’s just the way it is - when quite is used with an adjective before a noun, it comes before a or an.