Are the phone numbers called for references? Need to be on letter itself?

I have gotten some very high profile references to write me a letter. Director/SVP at FAANG and C suite at unicorn startups.

Some preferred not to list their personal phone numbers but gave their email addresses and the phone number of HR for each company, who can forward requests as needed. They also asked preferred that Tech Nation contact them via email.

Is this ok? I used docusign and have them signing from their corporate email addresses. I will list the HR numbers, but is Tech Nation going to call?

Also, I forgot to list the cell numbers on the signed letter, but I listed it in the application to submit. Is this ok, or I need to go back, edit the letter, and include their phone number? It took forever to get some of these people to write the reference, so I am hoping I can just submit now and list the phone numbers on the application form.

Their email and LinkedIn profile should be okay

Someone once reached out to the tech nation help desk and got a similar response. You can check it out here