Okay. This is a bit of a tough one. But I will dig in a bit so that hopefully, things will be clear.
Google figured out years ago that spam sites are all related and that relationships between sites can be determined. In science, the term realm is used to define a relationship between entities. In search, at least in the early days, a realm was a set of domains and sub-domains with a direct relationship. Obviously, example.com, www.example.com, and sub-domain.example.com can be related into a single realm. Over time, this changed so that site registrations, IP addresses, hosts, registrars and any information could also be used to add other related domains into a sites realm. Since then, this could also include smaller items such as e-mail addresses, phone numbers, authorship (not always), template usage, and so on to indicate relationships. Content between sites and language similarity can also be an indication. For example, it is possible to identify authors without a name associated with the work. Not everything Google will find will be clear, however with enough signals, Google can find relationships between sites rather well. They have a fair amount of experience these days.
So Google is looking for relationships between sites in the hopes of fighting spammers.
However, this is not a show-stopper. Not yet.
Site quality is paramount. So is branding. Google understands that there are companies that assist people within a specialized niche. Unfortunately, not all of these companies are completely honest. This can be especially seen in sites designed for attorneys. As well sites created using creation tools such as WIX can be a particular problem.
You will want to make sure of a few things. First, make sure your company site is well branded. I count 46 metrics associated with branding- too many to list here. The big elements are schema.org mark-up for company contact information that is easily found using a traditional page such as About or Contact or even in the site footer. It is best to have as much contact and location information as possible. As well, companies have a Products or Services page or another clear indication of doing business. Brands also have Acceptable Use Policies (AUP), Privacy Policies, Terms of Service (TOS) policies, and so on. At least one of these should exist. Also, sometimes personnel profiles exist. Think about what elements a company would have on their website and provide as many ordinary signals as you can.
Also, make sure your registration is not private and the registration contact information matches at least somewhat contact information on the site. This can be as small an e-mail address, phone number, or as large as the snail-mail address. You will want to do this for your customers too.
Make sure the company domain has good trust scores. I count over 50 metrics- again too many to list. The big ones are site age, registration information including company/contact information that is not tied to spammers, quality registrar, quality host, outbound links, content quality, SERP performance, and a clear history of doing the right thing. You will want to do this for you clients as well. Adding SSL can really help too. Just make sure it is from an high quality issuer that vets it's clients. It is not a necessity, but does go a long way to say this site is reputable.
As well, you do want to tie your client sites to yours as much as you can. Spammers do not make things easy for search engines so clear links between sites can really help to indicated honesty.
The Google rules say that site-wide links are a "no no". Google pulls back from this making the entire topic muddy. It is okay to make natural links. Google understands this. Their advice is to do what any reasonable well intentioned webmaster would do. I advise creating some indication that the sites were created by your company. A citation (mention) is enough. You do not actually have to create a link. I would avoid creating site-wide links. However, simple text on the bottom of the page can really help.
It is advisable to create indications of relationship between sites and make sure each site is behaving well. You will want to avoid over optimization. One step over the line can effect other sites. So for this, just make sure that your SEO work for your company and customers sites are honest and not to close to the line.
Because there is overlap in the metrics between spam sites and good companies creating niche business sites, it is important to conduct good business. However, this does not mean that you will be found to be a spammer. It just means that you have to be careful. The key is to be clear about your business, behave well, and to make sure that you are hiding as little as possible. Google really is fair and wants to help you succeed.
Here are some answers I have written that might help with background knowledge. These will not cover everything you need to know, but it will spark the imagination somewhat.
How semantic links work.
Why would a website with keyword stuffing rank higher than one without in google search results?
Establishing relationships between sites.
Multiple sites, same markup, different content, tier linkage = SEO penalty?
How to get Google PageRank (from the toolbar) to increase from 0?
Site wide links.
Do 'Created By' links add values to my website?
Please, let me know if you have additional questions, ideas, or concerns. I am here everyday and will be glad to help as much as I can.