"The" pixel does not exist as an SI approved measurement unit.
Now the issue is I was checking online and found a few 'convert from pixels to millimetres' and they come up with 92mm x 132mm.
Can you give the URL of such a website? 'Cause I'm gonna send them a mail: "You, Sir, are an Idiot to offer this."
A simple experiment will prove my point. Please indulge me: draw a rectangle in Photoshop 350 pixels wide by 500 pixels deep. Make sure to have the zoom set at 100%. Now take a ruler and measure the size of this rectangle is in millimeters.
Does that give you a calculation for "pixels to millimeters"? Of course it does, but only for your own screen. What you are measuring then is your local screen dpi. I could do the same and get another "real world size" because I'm positively sure my screen has a different number of dpi than yours, and the screen of the web "master" of "convertFromPixelsToMillimeters.com" will have yet another number of dpi.
It's a shame you are most likely using a modern LED or LCD screen, because with an ol' analog monitors I have an even better example: by fiddling with the dials on the front, you can expand or contract the electron beam to make your local view bigger or smaller. But the number of pixels stays the same!
Which one is correct? And why is Photoshop saying one thing and the online converter another?
Photoshop is correct. It is the only software in which you tie dimensions in pixels to a number of pixels per measurement unit -- and at that point, it's simple math.
If you are asked to design an ad of 350 x 500 pixels, don't worry about anything of the above. Those are the values to enter in Photoshop -- "dpi" values are inconsequential for the web.
(You would need to worry if you got contradicting instructions such as "3.5 x 5 inch, oh yeah and it's for the web by the way".)
There is another issue at hand which I overlooked in that longish story.
You are creating this ad in InDesign, and you can set ID's'measurement units to 'pixels' -- but Adobe's implementation is a bit shoddy. In fact, personally I feel that offering pixels in InDesign was a huge mistake! In Photoshop you can tie physical and pixel dimensions together because you can (actually, must) enter a dpi somewhere; in InDesign you cannot.
So after you created your advert and exported it to a web compatible format -- JPEG or PNG --, open it into Photoshop and check if the pixel dimensions are in fact correct.
I sent them this:
Offering a pixels-to-mm conversion -- in fact, *any* conversion of pixels to a real world measurement unit -- is plain wrong. The 'size' of a pixel depends only, and entirely, and per definition, on the local screen DPI.
You can only do a valid calculation if this same dialog also requires one to input a value for 'dpi'.
I didn't tell'em they are idiots -- I'm feeling Friendly today
...Or just design the thing in Photoshop and ignore InDesign. For a 350 px by 500 px design, there is not really any feature in InDesign that is not in Photoshop (except SWF). You don't need bleeds, multiple pages, output of live vectors, etc...