Ok, seeing as you ask me this directly, I'm going to answer directly.
Before you read this, please understand that I am trying to help you.
You noticed yourself that you didn't receive an answer to an almost identical question in another forum, so please read this with an open mind.
The bad part:
Your question is unclear.
You appear to be asking something about the different ways your page behaves in Mozilla browsers and Webkit based browsers, but having read the question three or four times, I am still unclear as to what.
I opened your page in both the latest version of Firefox and the latest version of Chrome and clicked on the right hand photo in each.
However, I couldn't determine any difference in either browser's behaviour.
You then proceed your question with two statements, each in brackets.
I don't understand these or how they contribute to the matter in hand.
You use abbreviations throughout your post, which make it difficult to read.
You then link to a long JS file with no indication of what this has to do with the problem.
What you can do better
Make a bare-bones page:
Take the page where the problem lies.
Strip out all unnecessary CSS styles.
Remove all unnecessary elements and content from the page (e.g. the side bar, the social media buttons).
To demonstrate your problem, you will only need two photos, so remove the unecessary photos, too.
In your post:
Provide a link to the bare-bones page you made.
Then ask your question and keep it focused.
I know this is difficult, but you could write something like:
"When I click the right hand picture in a webkit-based browser, I see an arrow icon pointing to the right once the next picture has loaded. When I do the same thing in Firefox, I don't see the icon until I move the mouse. Why is this?"
Don't use abbreviations such as "plz", "u", "thanx" etc.
Also don't use capital letters to make a point. The reader feels like they're being shouted at.
I am aware that you might not be overly technically minded and that posting on a forum might be a bit daunting.
I am also aware that English might not be everybody's first language.
However, following what I have written above will vastly increase the chances of you getting help.