Subsites pages indexed by Google as main site's pages

Hi,

I have a multisite install, let’s say https://www.multisite.com. I have some subsites, with domain mapping. Let’s say the subsite “subsite1” is mapped to https://www.subsite1.com

I’ve noticed that, although I have domain mapping all the websites in the multisite network (subfolder install), the subsites appear in the google index for the main site.

That is, if I type in google: site:www.multisite.com (the main site for the network), in the results I see something like this:

https://www.multisite.com/subsite1/ the subsite mapped to https://www.subsite1.com

How can I prevent this? I don’t want the subsites appear as being pages from the main’s website.

Including “Disallow: /subsite1/” in robots.txt is a good idea?
Will it prevent the mapped subsite to be indexed? Will it hurt their SEO?

Thanks in advance.

PS: the subsites in the mapped domains are indexed ok. That is, the query site:www.subsite1.com returns all the pages in the subsite. This is not a problem.