Your question isn’t clear about what exactly content you are placing within your startup tagged Passage, and what content is within the ‘other’ Passage, And when you say IE do you mean the Internet Explorer web-browser?
I created a new test project that consisted of the following two Passages:
1: A passage named Start which was marked as the ‘Start Story Here’ passage. I placed the line of text from your example within it.
Enter a Name then click START
2: A passage named Startup which I assigned the startup tag to.
I placed the following code within it as a test, although normally you would NOT put textual content within this passage as its purposed is for initialising variables.
Where variables get initialised.
(set: $variable to "value")
I tested the story in a number of web-browsers and I didn’t see the doubling up of the “Enter a Name then click START”. I didn’t test Internet Explorer because that’s not a supported web-browser.