You are interpreting theses passages according to your beliefs. You should really let the words of Jesus speak for themselves without interjecting your flavor of belief.
If Jesus said they believed, then without a doubt, they believed. Nothing is even remotely suggesting believing in name only. This is your interjection. You can't add to the Bible to make it say what you want. You will never come to the full truth that way. You must take what is said and believe it (and not with a nominal faith).
So, I ask, do I believe Jesus when He said they believe, or do I trust your interpretation with interjected words?
The word nominal is a theological term invented by man. Because if a man believed and fell away, it would destroy your doctrine. And Calvinists can't have that. They must cleverly invent some other meaning than what is actually taught.
I care not what Calvinism teaches. I find it more inventive than Thomas Edison. I do know what is brought out from Calvinists on this board. That is all I need to know about it. I can never have faith in a system which cannot, nor will not, take the passages from the word and believe them as they are presented (this is true nominal faith).
I have given passages from Ezekiel and James which, not one Calvinist will believe what it says. Why would I will myself to trust a belief system which will not hear, understand, apply, and obey the truths in God's word?
To prove what I am saying, I will ask you this:
Do you believe, understand, and obey the words of Ezekiel 18:31? Have you cast away your transgressions to make yourself a new heart and new spirit? A yes or no will suffice.
As one who trusts and believes the truths God has given us, I can say yes without any reservations. Can you do the same?