"Now that I think of it" vs. "Now that I have come to think of it&

I came from the Philippines and I’ve been using “Now that I think of it.” ever since. When I used it a while ago, someone I knew told me they don’t mostly use it here in America. He said Americans usually use “Now that I have come to think of it.”

Is it true?

No, not true. Is this person a native speaker?

All of these are possible informal utterances, Aikuzo:

Now that I think of it
Now that I come to think of it
Now that I’ve come to think of it
Come to think of it

Only the full ‘I have come’ is unexpected.

He’s not a native speaker. Hmm… I’ll probably just use “Now that I come to think of it.” from now on… xD